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THE SPECIALISTS' SERIES. 



ELECTRIC TRANSMISSION 
OF ENERGY 

AND ITS 

TRANSFORMATION, SUBDIVISION, 
AND DISTRIBUTION. 

A PRACTICAL HANDBOOK 

BY 
GISBERT KAPP, 

•I 

Member of the Institution of Civil Engineers ', Member 
of the Institution of Electrical Engineers, 

WITH l66 ILLUSTRATIONS. 

FOURTH EDITION, THOROUGHLY REVISED. 

> • 

NEW YORK: 

D. VAN NOSTRAND COMPANY, 

23, Murray Street, and 27, Warren Street. 

RECEIVED,| 

AUG 2 5 191* I 

Library, Navj U 



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m 2® 1917 



PREFACE. 

During the time which has elapsed since the third 
edition of this book was published an enormous develop- 
ment has taken place in every branch of electric power 
transmission. The use of electricity for transmission of 
power over very long distances has become an accom- 
plished fact, as proved by the works at Lauffen, Rome, 
Genoa, and the large installation now in course of erec- 
tion at Niagara Falls ; transmission plants for moderate 
distances have been established in so many localities that 
work of this kind has become quite commonplace ; the 
use of electric mining machinery, and the equipment of 
ship-yards with electrically driven tools, has made fair 
progress ; the distribution of power from central stations 
has become an important and profitable source of revenue 
to the lighting companies ; the use of electro-motors in 
lieu of long lines of shafting in factories and mills is 
slowly but surely gaining favour, and last, but not least, 
the application of electric traction on tramways and rail- 
ways has progressed with giant strides. The subject has 
thus not only become more attractive and practically 
useful, but has been specialized to an extent which 
renders its complete treatment in a book of this size 
impossible. I had, therefore, to face the question, what 
parts, or how much of each part, should be omitted ? Two 
ways were open. I might attempt to give a little of each 



VI PREFACE. 

branch of the subject by cutting down the theory to a 
few pages, and devoting the rest of the book to a neces- 
sarily superficial description of examples of all the 
various applications of electricity to power purposes that 
are now in use ; or I might omit certain branches of the 
subject altogether, and treat the others by expounding 
principles rather than giving examples. For several 
reasons I have chosen the latter way. In the first place, 
as the book is intended for students and practical engi- 
neers, and as any number of illustrated descriptions of 
electric power plant can be found in the technical press, 
I preferred to curtail rather the descriptive than the 
theoretical part of the previous editions. In the second 
place, the tendency to specialize in practice has called 
forth a similar tendency in literature, so that there is now 
no call for any one book to cover the whole of this vast 
field ; and lastly, I wished to gain room in this edition 
for the treatment of multiphase currents in order to draw 
the attention of English engineers to a branch of electrical 
work which has hitherto not received sufficient recogni- 
tion in this country. 

These considerations have made it necessary to com- 
pletely re-write more than half of the book, and omit a 
corresponding amount of old matter. Thus, the historical 
account of power transmission, detailed descriptions of 
plants, comparison of electric with other systems of 
transmission, underground cables, electric tramways, and 
telpher lines, have all been omitted. If the amount of 
capital invested in one particular branch of power trans- 
mission be taken as a measure of its importance, then 
electric propulsion is undoubtedly the most important of 
our subjects. Nevertheless its omission in this book 
appeared to me to be justified on the ground that the 



PREFACE. Vll 

excellent works of the late Mr. Reckenzaun, and Messrs. 
Crosby and Bell, give far more information than I could 
have given in the limited space at my disposal. As 
regards underground electric lines, the valuable book by 
Mr. Russell has made my treatment of this subject like- 
wise superfluous. The detailed descriptions of transmission 
plants given in the third edition have been cut out for 
want of room, and the same reason has forced me to 
curtail very much the description of more modern 
examples. Information of this kind will be found in the 
technical press, the Frankfort Exhibition Report, Pro- 
fessor ITnwin's Howard Lectures, and my Cantor 
Lectures. 

The theory of continuous current machines has been 
somewhat extended, and that of alternators and multi- 
phasers has been added. In treating the latter I have 
adopted graphic methods wherever possible, in the hope 
that practical engineers will find them more handy than 
complicated analytical expressions. The chapter on the 
line has been considerably enlarged, especially as regards 
the law of most economical section. The description of 
generators and motors given in the last chapter is not 
intended to form a complete catalogue of the machines 
built by the best makers, but is merely a collection of 
some representative types, in order that the reader may 
gain information as to the general construction of 
machines used in electric power transmission. 

Westminster, August, 1894. 



CONTENTS. 

PAGE 
Introductory 1 — 21 

CHAPTER I. 

General Principles — Lines of Force — Relations between Mechanical 
and Electrical Energy — Absolute Measurements — Ideal Motor and 
Transmission of Energy — Practical Units .... 22 — 60 

CHAPTER II. 

First Electro-Motor — Professor Forbes' Dynamo — Ideal Alternating 
Current Dynamo — Ideal Continuous Current Dynamo — Siemens' 
Shuttle- Wound Armature— Effect of Self-induction — Experiments 
with Electro-Motors — Hefner- Alteneck Armature — Gramme Arma- 
ture — Pacinotti Armature — Electro-Motive Force created in any 
Armature 61—95 



CHAPTER III. 

Reversibility of Dynamo Machines — Different conditions in Dynamos 
and Motors — Theory of Motors — Horse-power of Motors — Losses due 
to Mechanical and Magnetic Friction — Efficiency of Conversion — 
Electrical Efficiency — Formulas for Dynamos and Motors 96 — 111 

CHAPTER IV. 

Types of Field Magnets — Types of Armatures— Exciting Power — 
Magnetic Circuit — Magnetic Resistance — Formulas for Strength of 
Field — Single and Double Magnets — Difficulty in Small Dynamos — 
Characteristic Curves — Pre -determination of Characteristics — Arma- 
ture Reaction — Horse-power Curves — Speed Characteristics — Appli- 
cation to Electric Tramcars , 112 — 151 



CONTENTS. 



CHAPTER V. 



Graphic Treatment of Problems — Maximum External Energy — Maxi- 
mum Theoretical Efficiency — Determination of best Speed for Maxi. 
mum Commercial Efficiency — Variation of Speed in Shunt Motors — 
The Compound Machine as Generator — System of Transmission at 
Constant Speed — Practical Difficulty . . . . 152 — 166 



CHAPTER VI. 

Classification of Systems according to Source of Electricity — Trans- 
mission at Constant Pressure — Motors mechanically governed — Self - 
Regulating Motors — Transmission at Constant Current — Difficulty 
of Self-Regulation — Motor for Constant Current made Self-Regula- 
ting — Application to Transmission over large Areas — Continuous 
Current Transformator — Transmission between two Distant Points 
— Loss of Current by Leakage — Theory — Commercial Efficiency — 
Conditions for Maximum Commercial Efficiency— Self -Regulation 
for Constand Speed — Practical Example .... 167 — 207 

CHAPTER VII. 

Importance of alternating currents for long distance transmission — 
Ideal Alternator— E. M. F. of Alternators— Effective E. M. F. and 
Effective Current — Clock Diagram — Self- Induction — Power — Dif- 
ferent Methods of measuring Power .... 208 — 242 

CHAPTER VIII. 

Self-induction in Armature — Effect of Armature Reaction on the 
Field — Best Frequency — Transmission of Power between two Alter- 
nators—Margin of Power — Influence of Capacity . . 243—286 

CHAPTER IX. 

Objections to Single Phase Transmission — Advantages of Poliphase 
Transmission — Baily's Motor — Arago's Disc — Ferraris' Motor of 
1885 — Effect of Rotary Field on closed Coil Armature — Theory of 
Rotary Field Motors— Magnetic Slip — Torque Diagram— Starting 
Power— Magnetic Leakage — Extension of Theory to Practical 
Motors— Power Factor— Efficiency— Examples . . 287—354 



CONTENTS. XI 



CHAPTER X. 

Single Phase Motor — General Explanation of its Working — Theory of 
Single Phase Motors — Self-induction necessary — Torque Diagram — 
Practical Examples — Starting Device . 355 — 369 

CHAPTER XL 

The Line — Relation between Capital Outlay and Waste of Energy — 
Most Economical Method of Working — Weight of Copper in rela- 
tion to Power, Distance, Voltage and Efficiency — Phase Rectifier — 
Weight of Copper required with Different Systems of Transmission 
— Material of Conductor — Stress in Conductor — Insulators — Joints 
— Lightning Guards 370 — 401 

CHAPTER XIL 

Examples of Dynamos and Motors — Crompton — Edison — Hopkinson 
— Wolverhampton — Siemens — Brush — Mordey — Kapp — Brown — 
Wenstrom — Thury— Oerlikon — A. E. G. Company of Berlin 

402—431 

List of Formulae 433—434 

Index 435—445 



ERRATA. 



Page 118. Line 7 from bottom for (p. 24) read (p. 37). 

,, 153. Line 11 from bottom for (p. 39) read (pp. 51 and 54). 

,, 157. Lines 12 and 13 from bottom read \/ E By = \/80 = 8*94. 

,, 171. Line 10 for " service " read " surface." 



195. Equation 33) read c = - g 



V> 



E 



sr+jt(g + y) + yg. 



305. Equation 62 read S = — 
373. Bead W — c \/ ' w q t k p. 



ELECTRIC TRANSMISSION OF ENERGY. 

INTEODUCTOEY. 

The transmission of energy and its transformation is the 
fundamental problem of mechanical engineering. No 
piece of mechanism yet devised is capable of creating 
energy, but all mechanism has for its object the trans- 
mission, transformation, and application of energy already 
existing in nature in a more or less inconvenient form. 
A seam of coal some thousand feet below the surface of 
the ground represents a vast store of energy, but to 
utilize this energy we require a most elaborate system 
of human labour aided by mechanical appliances to get 
the coal, bring it to the surface, and transport it to the 
place where, by means of a steam-boiler and engine, we 
transform the energy chemically stored in the coal into 
mechanical energy, which is then further transmitted 
and subdivided as may be required. Or take the case 
of a waterfall in some remote mountain region. There 
is plenty of energy in the water, but to utilize it by a 
turbine on the spot would be highly inconvenient. The 
nature of the ground may be such as to make the erection 
of a factory in that particular spot impossible, and, even 
if this were not so, the remoteness of the locality would 

B 



2 ELECTRIC TRANSMISSION OF ENERGY. 

make the carriage of raw materials to the factory, and of 
the finished products from the factory, so difficult and 
costly, that working under these conditions would be- 
come commercially impossible. If we wish to utilize 
the water-power we must place the factory at the 
nearest convenient locality and convey the water to it in 
a pipe under pressure. The two cases here cited are 
typical examples of the transmission of energy, but 
there is a distinction between them. In the former case 
we have transmitted not the energy as such, but merely 
the material from which energy may be obtained by a 
chemical process, namely, the burning of the coal. In 
the lump of coal the energy is, so to speak, stored up, 
and we may therefore consider the carriage of coal from 
one place to another as the transmission of stored energy. 
In like manner when we send a load of corn from the field 
to the farm we transmit stored energy, for the corn, if used 
as food for horses or other animal machines, is converted 
into energy to be usefully applied to farm work when 
and as required. The characteristic feature of this 
method of transmission is that, as with coal, a chemical 
process must intervene before the stored energy becomes 
available, that is, becomes converted into live energy. 

With the high-pressure water-main this is not the 
case. The energy remains all the time in the live form, 
and can be made available by purely mechanical means, 
such as a turbine or water-wheel. There is also this 
further distinction, that the energy must be, utilized at 
the same rate as it is transmitted. When we transmit 
energy in the stored form we may use it when we like 
and at any rate we like. Coal can be stored for an 
indefinite time and burnt on the grate of the steam-boiler 
at a rate corresponding exactly with the demand for 



INTRODUCTORY. 3 

power at the time. Provided we have sufficiently large 
bunkers we may daily transmit the supply of coal for a 
week or more and not use our engine at all, or we may 
get in a week's supply at once and use the engine every 
day. In this respect the transmission of energy in the 
live form is not so convenient. Exactly the same number 
of gallons of*water we take in per minute at the top end 
of the pipe must flow out per minute and into the turbine 
at the bottom end. We cannot store the water in the 
pipe, and if from some cause the transmission is inter- 
rupted the power is cut off. 

The electric transmission of power may be effected 
both in the stored and live form, though the latter is the 
method commonly understood by this term, and is also 
the more important. 

If we use a steam-engine and dynamo for charging a 
secondary battery we store work. Now let us put the 
battery on a cart and convey it to a place some distance 
away where power is required. We can there deliver 
the power by joining the battery by two wires with an 
electro-motor, and mechanically gearing the motor with 
the machinery to which power is to be supplied. Here 
we have an example of electric transmission of power in 
the stored form. It is, moreover, a method which has 
already found some application in the working of tram- 
ways. At a convenient place on the line is established 
a charging station, where, by means of steam-power and 
charging dynamos, current is forced through sets of 
secondary batteries, and thus work is stored in them. 
Suitable arrangements facilitate the handling of the 
batteries, so that each car as it comes in from the road 
may have its exhausted battery quickly withdrawn and 
replaced by one fully charged, after which the car takes 



4 ELECTRIC TRANSMISSION OF ENERGY. 

the road again. We have here really two systems of 
transmitting energy electrically ; first, the transmission 
from the dynamo into the battery, which takes place in 
the live form and over a very short distance, and secondly, 
the transmission of power in the stored form by means 
of the battery which is carried on the car all over the 
line. 

A similar system is used for the propulsion of small 
boats. Within the last few years electrically propelled 
boats and charging stations have been placed upon the 
Thames and other waters, and in some cases electric 
boats are carried by large vessels as part of their regular 
equipment. Where a vessel is already fitted with the 
electric light the use of such an electric launch is par- 
ticularly convenient, because the same dynamo which 
works the lights at night can be used to charge the 
battery in the launch during the daytime, so that the 
launch may at any moment be ready to be lowered into 
the sea, and may contain a sufficient store of power for a 
run of some hours' duration. When the launch is stowed 
away on deck its battery may also be used for lighting 
purposes. 

These examples will suffice to show that there is some 
application for the electric transmission of power in the 
stored form, but the question to be considered is whether 
this method is applicable generally or not. If distance 
of transmission were the only consideration the storage 
battery sent by railway or canal would certainly have 
an enormous advantage over the rival system of trans- 
mitting live energy over wires, because there is a limit 
to the distance in the latter case, whilst there is no such 
limit in the former. But cost is a not less important 
consideration than distance, and it is impossible to say 



INTRODUCTORY. 5 

off hand whether in any given case transmission by wire 
will be dearer or cheaper than transmission by batteries. 
Each case must, in fact, be considered on its own merits, 
and for our present purpose it will suffice if we investi- 
gate in a general way the manner in which transmission 
of power by storage batteries could be carried out. It 
will be clear, to begin with, that if the original source of 
energy be coal, and if there be no objection to the 
establishment of a steam-engine at the place where the 
power is wanted, it will be better to carry coal there 
than charged storage batteries, because not only does a 
sack of coal represent more stored power than a battery 
of equal weight, but its transmission is easier, cheaper, 
and requires less precautions than that of the battery. 
If, however, the original source of energy is falling 
water, transmission by battery may be feasible. Let us 
see how such a system could be worked out. At the 
waterfall we establish a charging station, and to facili- 
tate the transport of the batteries we build a tramline or 
railway to the place where the power is required, say a 
factory, the machinery in which is worked by an electro- 
motor, which receives current from the batteries which 
are delivered there day by day, and when exhausted are 
returned to the power station for re-charging. The train 
which carries the batteries to and fro would of course 
also have to be worked electrically, and thus part of the 
store of power in the batteries would never reach the 
factory, but be expended for the purposes of transmission. 
The remainder would be given up to the motor at the 
factory, and the ratio of this amount to the total amount 
of work which could be taken out of the battery if it 
were discharged at the power station instead of at the 
factory would represent the efficiency of transmission. 



6 ELECTRIC TRANSMISSION OF ENERGY. 

If, for instance, the battery contains a store of 1,000 
horse-power hours, and the propulsion of the train re- 
quires 50 horse-power hours each way, then only 900 
horse-power hours remain available for delivery to the 
terminals of the electro-motor at the factory, and the 
efficiency of transmission w r ould be 90 per cent. The 
farther we can carry the batteries with a given loss of 
power (in this case 10 per cent.), or the smaller the loss 
over a given distance, the more perfect will be the 
system of transmission. Now it is evident that the 
degree of perfection to which we could bring this system 
of transmission must depend principally upon two points. 
First, the batteries themselves, and secondly, the road 
and arrangements for their transmission. The more 
power can be stored in a battery of a given weight and 
bulk, the smaller will be the fraction of this power which 
must be expended for traction, and the more, will remain 
for delivery. Again, the better and more level the road 
over which the transmission takes place, and the more 
perfect the propelling arrangements generally, the less 
power will be absorbed for the transmission of a given 
weight of batteries, and the more will remain for working 
the electro-motor at the factory. 

It is interesting to compare such a system of trans- 
mission with the well-known systems of transmitting 
stored power in the shape of corn and coal. In the case 
of corn the starting-point of our line of transmission is 
the field where the corn is grown (the ultimate source of 
energy being of course the sun). At the field we load 
the corn into waggons and send them to the farm, using 
horses as our propelling machines. But horses in order 
to work must eat, and they will eat the more of the corn 
the harder they work. Consequently a smaller amount 



INTRODUCTORY. 7 

of corn will be delivered at the farm than was taken 
from the field, and the ratio of these two quantities will 
be the efficiency of transmission, which must depend 
upon the kind of road available between the field and 
the farm, the nutritious value of the corn, the condition 
of the horses, and other considerations. If the efficiency 
of transmission is, as in the case of batteries, to be again 
90 per cent., then for every 100 sacks of corn taken 
from the field 90 sacks must be delivered at the farm, 
and the system will be the better the farther we are able 
to carry the corn with the expenditure of 10 sacks for 
every 100 taken from the field. 

The transmission of power stored in coal is a parallel 
case. At the pit's mouth we load the coal into waggons 
and haul them by means of a traction-engine or loco- 
motive to the place where the power is required. Part 
of the coal is consumed for traction purposes on the out- 
ward and homeward journey of the train, leaving the rest 
for the production of live power at the other end of the 
line of transmission. The less coal we spend for traction 
the higher is the efficiency of the system, or in other 
words, the farther we can carry the coal with the ex- 
penditure for traction of 10 tons out of every 100 tons 
taken out of the mine, the more perfect is our system of 
transmission. 

By tabulating the distances to which we can transmit 
stored power under different systems we can thus obtain 
a comparison as to their different values, as is shown in 
the following table. This table, reproduced from the 
author's Canton lecture, given at the Society of Arts in 
1891, has been calculated for three different lines of 
transmission, namely, an ordinary carriage road, a tram- 
way, and a railway. Each road is assumed to be level, 



8 



ELECTRIC TRANSMISSION OF ENERGY. 



and the best of its kind. The speed of transmission has 
been taken at 4, 8, and 20 miles per hour when coal and 
batteries are the transmitting agents for road, tram, and 
rail respectively, and at 4 miles per hour for all three 
kinds of road when the transmission of power is by means 
of corn transported by horses. 

Transmission of Stored Power. 



Source of Power. 


Distance in miles attainable with 
90 per cent, efficiency of trans- 
mission over 


Road. 


Tram. 


Rail. 


Coal and steam-engine . 

Corn and horse .... 

Storage battery and electro-motor . 


115 

52 
4 


270 

170 

10 


1,300 

440 

26 



A glance at this table will show that as far as efficiency 
of transmission is concerned, the electric system is far 
behind its two rivals. Even the primitive method of 
conveying the power stored in corn by means of a horse 
and cart over a carriage road is twice as efficient as an 
electric locomotive hauling storage batteries over a 
railway, and if compared with a steam locomotive hauling 
coal the difference is still greater. This low efficiency, 
and not less the great cost of batteries and their want of 
durability, form a great drawback to the electric trans- 
mission of stored power, and tend to restrict the applica- 
tion of such a method to cases where steam-power, 
animal-power, and other methods of transmission are for 
special reasons inapplicable. If it should be found 
possible to greatly reduce the weight and cost of storage 
batteries, and at the same time increase their durability, 
the electric transmission of power by their means might 
yet become commercially feasible, but, taking the batteries 



INTRODUCTORY. 9 

as we find them at present, they cannot compete against 
other methods of transmission. 

If we now turn to the electric transmission of live 
power the case is far more hopeful. Such a system of 
transmission consists of three essential parts. A gene- 
rating station where a steam-engine, turbine, or other 
prime mover, supplies mechanical power to a dynamo 
machine. This machine converts the mechanical power 
into electrical power, represented by a current flowing 
under a certain electric pressure. The current is con- 
veyed along the line of transmission, by means of copper 
wires, to the motor station, where the electric power of 
the current is, by means of an electro-motor, again recon- 
verted into mechanical power. We have thus the three 
parts, generator, line, and motor, which together con- 
stitute the transmission plant. The particular arrange- 
ments by which power is conveyed from the prime mover 
to the generator, and the corresponding arrangements by 
which the power is delivered from the motor, are not, 
strictly speaking, part of the plant by which the electric 
transmission of power is effected, although they are 
necessary adjuncts of the system of transmission taken as 
a whole. 

Going back to our example of the waterfall, and the 
way in which the power, represented in the falling water, 
can be utilized- for driving a factory or mill, it will be 
immediately clear how, by the use of dynamos and con- 
ducting wires, the distance of transmission can be ex- 
tended. We have assumed that the waterfall is situated 
in some remote mountain region which in itself is not 
adapted as a site for the mill. Hence it was useless to 
erect the turbine at the fall itself, but we had to take the 
water in a high-pressure main to the nearest place where 



10 ELECTRIC TRANSMISSION OF ENERGY. 

a mill and turbine could be conveniently erected. The 
distance over which water can thus be made to transmit 
power is limited by the cost of the pipe or other kind of 
aqueduct, and by the loss of head due to friction. If, 
then, instead of having to build a costly aqueduct, we 
need only put up a pair of copper wires supported on 
insulators and poles, it is obvious that the line of trans- 
mission will become cheaper, and, consequently, that we 
shall be able to afford a longer line, if local conditions 
should render it desirable to place the mill further away 
from the waterfall. We see thus that electric trans- 
mission offers a means for the utilization of natural 
sources of power which, by reason of their remoteness, 
could not be reached by any other method. Of these 
natural sources, coal, wind, and water, are the most 
important. 

As regards the first-named source of power, electric 
transmission is as yet rather a matter of the convenient 
application and subdivision, than the utilization of some 
natural source of power which would otherwise be wasted. 
We drive railways and tramways by electrically trans- 
mitted power, which power is originally due to the 
burning of coal. As far as economy of fuel is concerned, 
the use of separate locomotive steam-cars may not be less 
advantageous than that of cars propelled by electro- 
motors, but we employ the latter in preference because 
of their greater convenience and the absence of noise, 
heat, dirt, and smoke, so objectionable in underground 
railways and town tramways. Similarly we may replace 
in machine shops the long lines of main shafting and belt, 
or other gear, by small electro-motors, each driving its 
own tool, but we do this simply as a matter of convenience 
and to prevent the waste of power involved in these 



INTRODUCTORY. 11 

mechanical methods of transmission. Here it is not a 
question of utilizing a source of power which hitherto 
has been inaccessible. We must bring coal to the 
railway or factory whether we use a large steam-engine 
or a number of small ones, but in the former case we 
burn less of the coal to do a given amount of work, and 
are able to subdivide the power more conveniently. 

Again, if we employ electric transmission of power in 
coal mining, it is not so much on account of its greater 
efficiency as compared with transmission by compressed 
air or water under pressure, but by reason of its greater 
convenience and the smaller capital outlay for plant. 
Whether the time will ever come when the power derived 
from coal will be electrically transmitted over long dis- 
tances, as is now the case with water-power, it is impos- 
sible to predict. It has been suggested to erect large 
electrical generating stations close to the pit's mouth, 
and there produce current by steam-power obtained from 
the small coal which is not worth being carried by rail. 
The current would be transmitted by wire to industrial 
towns in the neighbourhood where power is required, and 
thus the energy contained in the refuse of our coal-fields 
could be utilized. As yet this suggestion has not been 
carried out, probably because continuous currents, which 
have up to the present been almost exclusively considered 
in connection with transmission work, are not adapted 
for very long distances. Within the last few years con- 
siderable progress has, however, been made in electric 
transmission of power by means of alternating and multi- 
phase currents, and it is possible that with further im- 
provements in the same direction these various systems 
may become available for the supply and subdivision of 
power throughout towns some twenty, thirty, or more 



12 ELECTRIC TRANSMISSION OF ENERGY. 

miles distant from the coal-field where the power is 
generated. 

This is, however, a problem of the future. For the 
present we may be satisfied to utilize those water-powers 
which would otherwise be running to waste. Even with 
this limitation the field for the use of electric transmission 
of power is very wide. To take only a few examples. 
The falls of the Rhine at Schaffhausen represent about 
1,750,000 horse-power. Niagara is computed by the 
Cataract Company to represent some 5,000,000, though 
Herr Japing estimates it at 16,000,000 horse-power. 
According to M. Chretien, a French engineer, the total 
water-power in France is 17,000,000 horse-power. Com- 
pared with such figures the amount of horse-power 
derived from coal is small. The total consumption of 
coal within the United Kingdom is about 150,000,000 
tons annually. 

A Royal Commission, sitting in 1870, estimated that 
44 per cent, of the total is used in mining and metallur- 
gical work ; 26 per cent, is required for domestic purposes, 
such as heating, gas, and water supply ; 5 per cent, for 
locomotion ; and 25 per cent, for manufactures. In this 
latter item is included the use of coal for the generation 
of steam-power. If we allow four-fifths of this, or 
30,000,000 tons, exclusively for steam-power, it will be a 
liberal estimate, and reckoning an average of 5^ lbs. of 
coal per horse-power hour, and 3,000 hours as the average 
working time of steam-engines throughout the year, we 
find that the total steam-power in use in the United 
Kingdom is about 3,500,000 horse-power. This calcula- 
tion is, of course, very rough, and is only made to show 
of what order the figure is representing the power derived 
from coal. If we put the steam-power in use in America 




INTR OB UCTOl&mO^^ 1 1 3 



and the rest of the world at twice the above figure we 
find that the steam-power in use throughout the world 
does not much exceed 10,000,000 horse-power, which is 
less than the water-power of France, and, of course, only 
a very small fraction of the total water-power throughout 
the world. 

As far as power alone is concerned the world, taken as 
a whole, could therefore very well afford to do without 
coal, although individual countries could not. But even 
in those countries where water-power is abundant it 
would be useless if we had not some economical means 
for transmitting it to considerable distances, and it is in 
this respect that electric transmission has become of so 
much importance of late, because it enables us to utilize 
sources of power which would be otherwise running to 
waste. It is natural to expect that power transmission 
generally will become most developed in countries where 
fuel is dear and waterfalls abound. This is actually the 
case in Switzerland. This country produces no coal and 
the supply of wood is not even sufficient for domestic 
use, so that steam users depend entirely on imported coal, 
the total value of which is estimated at £800,000 annually. 
Here we have all the conditions which tend to the better 
utilization of water-power, and it is therefore natural that 
Switzerland has, ever since it became an industrial 
country, paid great attention to the problem of how to 
get power from waterfalls, and how to transmit this 
power to the place where it can be used to greatest 
advantage. 

The first system of power transmission to a distance on 
a large scale was the outcome of experiments made in 
1850 by Ferdinand Hirn, in Alsace, who succeeded, by 
means of flat steel ropes, in transmitting power to a dis- 



14 ELECTRIC TRANSMISSION OF ENERGY. 

tance of 80 and later of 240 metres. The success of these 
installations was so marked that engineers quickly took 
up the new system, and within ten years there were, in 
South Germany and Switzerland, some 400 transmissions 
at work, conveying an aggregate of 4,200 horse-power. 
The original flat steel ropes had, however, been replaced 
by round cable running over pulleys with V-shaped 
grooves. In 1863 a transmission plant of considerable 
magnitude was proposed by Herr Moser of Schaffhausen, 
with a view to utilize the power of the Rhine for indus- 
trial purposes. By means of a weir placed across the 
river a fall of from 12 to 16 feet was obtained, and a 
turbine station established on the left bank. Three 
turbines, each of 750 horse-power, were erected, and the 
power was carried across the river and along the right 
bank by cables to the various mills and factories in Schaff- 
hausen, who took it at a fixed rental of from £5 to £6 per 
annum per horse-power, according to the greater or lesser 
amount of power contracted for. This transmission is still 
at work, though part of it has been replaced by an electric 
transmission plant erected for the " Kammgarnspinnerei" 
about three years ago by the Oerlikon works. The 
annual charge per horse-power is now only £2 16s. 

The fact that so well designed a work as the Schaff- 
hausen teledynamic transmission is being superseded by 
electric transmission, shows that the latter must have 
considerable advantages over the former. Although 
wire-rope transmission is exceedingly simple and positive 
in its action, it becomes unwieldy when the power 
exceeds 600 horse-power, and the distance over which it 
is economical is limited. The great cost of the cable 
towers, the influence of temperature on the strain in the 
cable, and the rapid wear of the latter are also serious 



INTRODUCTORY. 15 

drawbacks, and although teledynamic transmissions have 
been erected and are still working in other places, such as 
Bellegarde, Freiberg, and Zurich, it is doubtful whether 
the system will be able to permanently hold the field 
against its electrical rival. At the present time several 
thousand horse-power are already being transmitted 
electrically in Switzerland alone, and the system is being 
rapidly extended. 

If we look to the United States as another country 
abounding in water-power, we find that its advantages 
are there also largely appreciated. According to a 
census in 1880 the total water and steam-power in use 
in the United States was 3,400,000 horse-power, of which 
1,225,000 horse-power were furnished by water. Bearing 
in mind that this census was taken twelve years ago, 
when transmission of power as we now understand it was 
but little developed, it follows that the bulk of this water- 
power was utilized locally, and that there must be a far 
larger amount of yet undeveloped water-power capable of 
being brought into use by means of electric transmission. 

In Great Britain there is, of course, not so much scope 
for electric transmission of water-power, partly because 
waterfalls of any dynamic magnitude, and which are not 
already brought into use, are scarce, but principally 
because coal is cheap. There are, however, also here 
some very successful examples of electric transmission, 
amongst which may be mentioned the electric railways of 
Portrush, and that between Bessbrook and Newry. 

With us electric transmission is of importance, not so 
much on account of its ability to bring into use hitherto 
inaccessible sources of power, as on account of its con- 
venience for the subdivision aud application of pow r er 
generated at some central point. 



16 ELECTRIC TRANSMISSION OF ENERGY. 

In these cases the power is obtained from coal, and 
although its cost is, generally speaking, higher than that 
of water power, its electric transmission, and especially 
its subdivision, constitutes still an economy if compared 
with the use of many small steam-engines having col- 
lectively the same power as the large engine at the 
central point. This is due partly to the greater effi- 
ciency of the large steam-engine, and partly to the fact 
that the cost of attendance is reduced. Where each 
small user of power is obliged to have his own boiler and 
engine, an attendant must be employed to stoke the 
boiler and drive the engine ; but where the power is 
supplied electrically no special attendant is required. 
Beyond occasionally oiling the bearings of the motor 
and turning a switch to start or stop the motor, no 
attention is required. There is the further advantage 
that the space occupied by the motor is insignificant as 
compared with the space required for boiler, engine, 
feed-tanks, coal bunkers, etc. ; that it can be put into 
any convenient position, and that its efficiency over a 
wide range of load is very high. The ease with which 
an electric motor can be stopped and started also tends 
to economy, because the motor need never be left 
running idle. With a steam-engine — and still more so 
with a gas-engine — the reverse is the case. The starting 
requires a considerable amount of skilled labour, and the 
result is that stopping and starting is avoided as far as 
possible, the owner, where the work is intermittent, pre- 
ferring to run the engine through the idle periods rather 
than go to the trouble of starting up afresh each time 
that power is wanted. There are other advantages 
which the electric motor has over local engines, such as 
higher efficiency at light loads, freedom from heat, noise, 



INTRODUCTORY. 17 

danger of explosion, and greater cleanliness, all of which 
are so obvious as to need no further comment. 

Reference has already been made to the use of motors 
in factories, and as within the last few years this applica- 
tion of electric power has been greatly developed, a few 
words of further explanation may here be given. Not 
only are cranes, lifts, and travellers worked electrically, 
but in many of the best-equipped works the machine 
tools are driven by motors which are supplied with power 
from a central generating station. The advantages of 
using electric motors for driving machine tools are mani- 
fold. In the first place we have greater economy. The 
large central boiler plant can be provided with mechani- 
cal stokers, and thus a cheaper class of coal may be 
burned, and the number of firemen reduced. A steam- 
engine of the most economical type may be used, which 
would not be possible with a number of smaller engines 
erected in different parts of the works. In the next place 
there is a saving in power due to the absence of long 
lines of shafting, and, most important of all, we do away 
with all or nearly all the belting which obstructs the 
workshop and involves a considerable expense for upkeep. 

In applying electric transmission of power to engi- 
neering shops two systems may be used. We may either 
provide each machine tool with its own motor, or we may 
have one motor and a short length of counter-shafting to 
drive two or three tools. The former system is adopted 
where the tools are large and require each an appreciable 
amount of power, and the latter for small tools, especially 
if it be possible to so group them that they will generally 
have to be worked together. How far such grouping of 
machines should be carried is a matter which has to be 
considered carefully in each case. By putting several 

c 



18 ELECTRIC TRANSMISSION OF ENERGY, 

machines on to one motor we may get a slightly higher 
efficiency in the motor when all the machines are at 
work, and we reduce the capital outlay. On the other 
hand we have more belts and shafting to look after, and 
the " over all" efficiency of the plant during the time that 
some of the machines only are being used is lower. The 
modern tendency is in the direction of using separate 
motors for all except the smallest machine tools. The 
over all efficiency of this system as compared with that 
of long lines of shafting with fast and loose pulleys, 
belts, bearings and geared wheels is very high. The 
reason is that only those motors need be supplied with 
current which at any time are required for working the 
machine tools, and that the amount of power which must 
be supplied electrically is approximately proportional to 
the work done. With mechanical systems of transmission 
this is not the case. Whether all the tools or only a 
few of them are required at any time, the whole of the 
shafting and other gear must be kept in motion, and the 
power wasted in friction remains almost constant. Hence, 
at times when only a few of the tools are being worked, 
the over all efficiency of this method of transmitting 
power becomes very much lower than the electric trans- 
mission. The latter has, further, the advantage of being 
extremely flexible and easily installed. 

No mechanical force can be detected in the conductor 
carrying the electrical energy such as appears during 
purely mechanical transmission with shafting, belts, wire- 
ropes, or in pipes conveying steam, water, or air. The 
conductor is clean, cold, does not move, and altogether 
appears inert. It can be bent, moved, or shifted in any 
manner while transmitting many horse-power. It might 
be brought round sharp corners, and, having little weight, 



INTRODUCTORY. 19 

it can be fixed with greater ease than any mechanical 
connection. It is thus possible to bring the energy into 
rooms and places awkwardly situated for mechanical 
transmission, and there is no noise, smell, dirt, or heat 
during the transit, nothing to burst or give way. The 
power is, moreover, under perfect control, and its appli- 
cation exceedingly elastic. The same circuit which is 
used for supplying light, and may be tapped to give 
many horse-power, can, at the same time and as con- 
veniently, be used to work a sewing-machine or other 
small domestic implement, and the power consumed at 
the generating dynamo is always in proportion to the 
power obtained from all the motors, so that there is no 
waste of energy if some of the motors are standing still 
or are working with less than their full load. 

Another and a very important application of electric 
power concerns the propulsion of vehicles. Allusion has 
already been made to some electric railways where a 
water-fall is the original source of power, which latter is 
transmitted electrically to the train ; but even where the 
power is originally derived from coal its electric trans- 
mission may be of advantage in certain cases. Thus, for 
working street tram-cars we might employ cable traction 
or small locomotives, but neither method is so convenient 
as electric traction. Anyone who has seen the electric 
cars in the crowded and tortuous streets of Boston (Mass.) 
must realize that neither the horse, the cable, nor the 
steam locomotive could cope with such an enormous 
traffic as easily as the electric motor, to say nothing of 
the great cost and technical difficulties of establishing a 
cable system in the centre of the town, and the objection 
to the use of steam locomotives on account of dirt and 
noise. The electric cars take sharp turnings with the 



20 ELECTRIC TRANSMISSION OF ENERGY. 

greatest ease, and are, as regards speed, under perfect 
control, whilst they occupy less space than horse or 
steam-cars, which in crowded streets is a great con- 
sideration. The only objection — but this is a very serious 
one as far as England is concerned — is the overhead or 
" trolley wire " necessary to bring the current to the car. 
Hence, in this country, electric trolley cars have as yet 
only been used on suburban or rural lines. For town 
traffic the trolley is inadmissible, or at least has not yet 
been sanctioned by the authorities, and electric traction 
can only be obtained either by the use of an underground 
conductor and slot in the street, or by the use of storage 
batteries carried on the car. There is, however, another 
kind of railway in towns where electric traction is almost 
indispensable, namely, the underground lines running in 
cast-iron tunnels. Of this type the City and South 
London line has been the pioneer, and has now been 
running successfully for some years. The use of steam 
locomotives on a line of this type is of course out of the 
question, and although cable traction was at first pro- 
posed, it was abandoned in favour of electric traction, and 
the technical success of the line has proved the wisdom 
of this decision. Bills for similar lines crossing London 
in various directions have been promoted, and have re- 
ceived parliamentary sanction, and there can be no doubt 
that we shall shortly witness a large development of 
these underground electric railways. 

Thus electric transmission of power has invaded almost 
every domain of the mechanical engineer. We have the 
long distance transmission of power in bulk, so to speak, 
by means of which the energy of falling water at some 
place far back in the mountains is brought to the town 
for lighting, for driving mills, metallurgical works, and 



INTRODUCTORY. 21 

electric cars ; we have the central electric lighting 
station supplying current not only for lighting, but also 
for power to the small artizan ; we have the power-house 
and electric railway, or the mine with its generating 
station, underground cables, and electrically worked 
mining tools ; we have the dock with its electric cranes 
and hoists, and the workshop with its machine tools 
worked by electric current. 



CHAPTEE I. 

General Principles — Lines of Force — Relations between Mechanical and 
Electrical Energy — Absolute Measurements — Ideal Motor and Trans- 
mission of Energy — Practical Units. 

A proper understanding of the principle of the conser- 
vation of energy, which exists throughout the whole of 
nature, must necessarily form the basis of all scientific in- 
vestigation of mechanical or electrical problems, and of 
most of the improvements we might attempt to introduce 
in existing machinery and apparatus. In many cases, 
the fact that the original amount of energy remains un- 
changed, whilst the form in which it becomes manifest 
undergoes many alterations, is easily understood. For 
instance, if a locomotive engine draws a train behind it 
on a railway, we are at no loss to explain how the energy 
of fluid pressure of steam in the boiler is transformed into 
that of a steady pull overcoming the resistance of the 
train at a speed of so many miles per hour, and including 
all the so-called waste caused by deformation, friction, 
abrasion, and heating of the bodies through which the 
energy flows. The means by which, in this case, energy 
is transformed are, for the most part, purely mechanical, 
and sufficiently familiar to our imagination to allow us to 
form a mental picture of the different processes taking 
place. Even the transformation of heat into energy of 
fluid pressure, although we are not able to represent it by a 



LINES OF FORCE. 23 

mechanical model, has, through long familiarity with heat 
engines in one form or another, become comprehensible to 
us. With electrical energy, and with that of chemical 
action, this is not so. We can form no kind of mental 
picture of the process taking place in a voltaic cell where 
the energy of chemical action is transformed into that of 
an electric current, nor can we say what are the connect- 
ing links by the aid of which this current, after passing 
through hundreds of miles of wire, is made to impart 
mechanical energy to the armature of an electro-magnet, 
and thereby produce telegraphic signals. There is no 
mechanical connection between the sending key and the 
lever of the Morse instrument by which energy could be 
transmitted in the form of a pull, as is the case in our 
example of the coupling between a locomotive and its 
train, and yet energy is unmistakably transmitted. If 
we neglect waste, that is energy transformed in a way not 
immediately useful for the purpose in view, we find that 
the amount of electrical energy received at the distant 
station is proportional to the amount of chemical energy 
used up ; and if we take the waste also into account, we 
shall find that the energy it represents, added to that 
received in the form of an electric current at the distant 
station, is again proportional to the amount of chemical 
energy developed in the voltaic cell. If we know the 
nature of the chemical process going on in the cell, we 
can always calculate, by the aid of electro-chemical 
equivalents, what total amount of electrical energy can 
be obtained from a given weight of materials. 

Similarly there exists a definite and constant propor- 
tion between electrical and mechanical energy. The re- 
lation between the two is somewhat complicated by the 
development of heat, which, indeed, is inseparable from 



24 ELECTRIC TRANSMISSION OF ENERGY. 

electric phenomena, but if we make due allowance for the 
energy wasted in heat, we shall find that a given amount 
of electrical energy will always produce the same amount 
of mechanical energy, irrespective of the time required, 
or the exact manner of transformation. Although we 
cannot say what are the connecting links between electric 
current and mechanical force, experiment shows that cer- 
tain definite relations exist, and we can, on the basis of 
experimental facts, conceive a mental picture or model by 
the aid of which these relations are represented in a fami- 
liar form. Such a mental picture is the conception of 
magnetic lines of force, first introduced by Faraday. In 
adopting this method of rendering electro-mechanical 
phenomena tangible to our senses, we make no assump- 
tion whatever about the reality of the lines of force. 
Whether they actually exist is a matter of total indif- 
ference ; but since all the experiments we can make are 
compatible with that conception, and since it enables us 
not only to explain experimental facts, but also to bring 
them within the region of actual measurement and calcu- 
lation, it is convenient to make the theory of magnetic 
lines ef force the basis of electro-mechanical investigations. 
If a sheet of paper be laid over a straight steel magnet 
having opposite poles at its ends, and sprinkled with iron 
filings, it will be found that these arrange themselves in 
curves, which we take to be the magnetic lines of 
force, 1 Fig. 1. Each of these lines forms a closed curve 

1 A very convenient way of fixing these curves is by the aid of a sheet of 
glass, the surface of which has been coated with a thin layer of paraffin. 
The glass is laid over the magnet, then sprinkled, and carefully lifted off so 
as not to disturb the filings. It is then gently heated, when the paraffin 
melts, and upon cooling again the iron filings are fixed to the glass by the 
coating of paraffin. The glass plate may then be handled as if it were a 
drawing, and the curves can be reproduced by photography. The drawing 
in tb3 text has been obtained in this manner. 



LINES OF FORCE. 



25 



issuing from a point at one end of the magnet, and enter- 
ing at a corresponding point at the other end. Some of 
the curves extend far out into space, beyond the surface 
of the paper, and as far as they are visible, they 
appear as open lines growing fainter the farther we 
go from the poles. They must, nevertheless, be con- 
sidered to be closed lines, only so faint that we cannot 
trace them throughout their whole length. If the poles 
of our magnet were two mathematical points, all the 
curves would pass through those points, but since we 

Fig. 1. 






^-■y'-r 






^fc£v& 






'-'■^-'''y 


- v 'C\''->-' 


</;'«'l ;-'.'-,«••■'' ' 


' ' <■■■ '' ''~ 


; 






i^ff'yy- 


JH 


y/y~' : 



^W&¥M- 



have to deal with a physical magnet, the poles of which are 
surfaces of some extension, the lines issue from all over 
these surfaces. To investigate the magnetic properties of 
these lines we can use a long thin magnetic needle (a 
magnetized knitting-needle answers very well) suspended 
vertically by a long thread, so that the lower end of the 
needle is within a short distance of the paper, and free to 
move all over it. We shall then find that the lower end 
of the needle will be repelled by one pole of the magnet 
and attracted by the other, and in following the combined 
action of these forces, it will move along that particular 



26 ELECTRIC TRANSMISSION OF ENERGY. 

line of force upon which it was set on to the paper in the 
first instance, but it will never move across the lines. 
We conclude from this experiment that the lines of force 
are paths along which a free magnet pole is urged under 
the influence of the magnet. A free magnet pole of oppo- 
site sign would travel along the same lines, but in opposite 
direction, and, if of the same strength, it will be urged 
along with an equal force. If, instead of a long vertical 
needle, we take a very short one suspended horizontally 
in its centre close to the surface of the paper, the two 



Fig. 2. 



^ 



s 

7 r~\ 






*>Aji, 



opposite forces will tend to set the needle so as to form a 
tangent to the line of force passing through its centre, and 
as then the two forces are equal and opposite, no bodily 
shifting of the needle can take place. But on whatever 
point of any of the curves we set the needle, it will always 
swivel into such a position that its magnetic axis, that is 
a straight line joining its two poles, becomes a tangent to 
the curve. (Fig. 2.) It should here be remarked that 
unless the needle is very short in comparison to the mag- 
net it will, when placed near one of the poles, be drawn 
right up to it, because in this case there would be a sen- 
sible difference in the distance of either of its poles from 



CHAIN OF MAGNETIZED MOLECULES. 27 

that magnet pole, and consequently the opposing forces 
would no longer be in equilibrium. But if the needle is 
very short, say only the length of a particle of iron filing, 
this inequality between the attracting and repelling force 
will at a short distance from the magnet pole become 
omissible, and then the particle of iron filing will only set 
itself into the direction of the line of force in that place, 
but not move bodily along it. We may thus regard each 
particle of iron filing which has been sprinkled over the 
paper as a very short magnetic needle, and each line of 
force as a chain of such needles linked together by their 
poles of opposite sign — n x s x — n 2 s 2 — n 3 s 3 — and so on, as 
shown in Fig. 2. Imagine now that the particles in one 
such chain, whilst under the influence of the magnet, 
could by some process be suddenly hardened into steel, 
or that we had taken steel filings in the first instance, and 
then remove the magnet. We would then have a succes- 
sion of little magnets, whose poles of opposite sign touch, 
and therefore eliminate each other, with exception of the 
first and last particle of the chain. Here we would have 
a free N pole at one end, and a free S pole at the other 
end, these being a finite distance apart, and therefore 
able to exert magnetic action on other pieces of iron 
placed into their neighbourhood. But let each particle 
be turned round its centre (without however, shifting it, 
bodily) so as to break contact with its neighbour, and we 
shall have a disjointed line of very small magnets, (Fig. 3), 
none of which is able to exert any magnetic attraction or 
repulsion at a distance, because on account of the proxi- 
mity of the two opposite poles in each particle, their dis- 
tances from any external point to be acted on would be 
sensibly equal, and consequently the opposite forces 
would be in equilibrium. By turning each particle so as 



28 ELECTRIC TRANSMISSION OF ENERGY. 

to thoroughly break contact with its neighbour, we have 
completely destroyed the magnetic action of our chain at 
a distance. If we had turned only a few of the particles, 
or if we had turned all through a very small angle, so as 
not to completely interrupt their magnetic continuity, the 
magnetism of the chain as a whole would have been 
weakened but not destroyed completely. We can restore 
our magnetic chain again by turning each particle back 
into its original position, and if this process should be too 
laborious to be performed by hand, we can accomplish it 
in an instant by replacing our magnet under the paper, 

Fig. 3. 



1*4 



'/ l 



when its line of force corresponding to the chain of 
particles, will pass through it again and swivel each into 
a tangential position, whereby poles of opposite sign are 
again brought into contact, thus eliminating each other, 
with the exception of the two free poles at the ends of the 
chain. 

According to the modern theory of magnetism l as de- 
veloped by Weber, Wiedemann, Hughes, and others, 
what has here been described for a chain of iron filings 
lying on the sheet of paper, actually takes place within 

1 Proceedings Royal Society, May 10, 1883; also a paper on "The 
Cause of Evident Magnetism in Iron, Steel, and other Magnetic Metals," 
read before the Society of Telegraph Engineers and EJectricians, and 
reported in their Journal, vol. xii., No. 49. 



PROFESSOR HUGHES^ THEORY. 29 

the body of any piece of iron or steel whilst being 
magnetized. According to this theory, each molecule 
of iron or steel is a complete magnet ; it is provided at 
one end with a definite quantity of magnetic matter of 
one sign, and at the other end with precisely the same 
quantity of magnetic matter of the opposite sign, and 
these magnetic charges are an inseparable attribute of 
matter like its gravity or chemical or thermal properties, 
and they can neither be increased nor diminished. In an 
unmagnetized bar of steel these molecular magnets are 
supposed to form either chains closed in themselves or 
disjointed chains, their magnetic axes pointing in all 
possible directions, and therefore, as was the case in our 
chain of iron filings after we had rotated them, incapable 
of magnetic action at a distance. But if, by some means, 
it were possible to turn all the molecules so as to point 
one way, without, however, displacing them bodily, we 
would obtain a number of parallel magnetic chains 
showing free magnetism at their ends only, and there- 
fore capable of exerting magnetic attraction and repulsion 
at a distance ; in other words, our bar of steel would 
become a magnet. It will be seen that according to 
this theory the molecules composing a bar of magne- 
tizable steel must be capable of rotation around their 
centres, and the more easily and completely they can be 
rotated, the greater is the degree of magnetization ob- 
tained. Since we cannot take hold of each molecule and 
rotate it mechanically, we must adopt the other method, 
viz., that of sending lines of force through the bar to 
perform that work, as we did with the chain of iron 
filings. This can be done either by the aid of another 
magnet, or by an electric current. The setting of mole- 
cules into continuous chains will be the more complete, 



30 ELECTRIC TRANSMISSION OF ENERGY. 

the less resistance or internal friction they offer to rota- 
tion, and the more powerful are the lines of force which 
are caused to pass through the bar of steel. In very soft 
steel, or in soft iron, the molecules rotate freely, and can 
be set almost completely into continuous chains, but the 
harder the steel the smaller is the angle through which 
each molecule can be rotated, and the more magnetizing 
force is required for this purpose. In such cases the 
magnetic chains are more or less discontinuous, and the 
magnetism appearing externally is weaker. On the other 
hand, the molecules once rotated into position of magnetic 
continuity are not so easily disturbed again, and thus the 
harder tfye steel the more permanent is its magnetization. 
In soft iron the molecules will lose their magnetic con- 
tinuity as easily as it was acquired, and the slightest 
mechanical strain or vibration is sufficient to destroy the 
greater part of the previous magnetization. To illustrate 
this we may take a glass tube filled loosely with iron 
filings, which can be magnetized by drawing the pole of 
a magnet along it. We shall then see that the particles 
of filing which previously were lying in all possible direc- 
tions, have now become more or less parallel to the tube, 
and the whole appears more like a solid piece of iron of 
very fibrous texture. The tube has now become a magnet, 
and if it be carefully handled so as not to disturb the 
arrangement of the particles, it can be used as if it were 
a solid steel magnet, and all the usual phenomena of 
attraction and repulsion at a distance can be obtained. 
But on tapping or shaking the tube the particles relapse 
into their former confused position, and all traces of ex- 
ternal magnetism of our tube vanish. From this short 
outline of Professor Hughes' theory it will be seen that 
the only way in which we can act upon the molecules in 



THE MAGNETIC FIELD. 31 

the interior of a bar of iron or steel is by sending lines of 
force through it. The greater the number of lines, or the 
more powerful the individual lines which we can force 
through the bar — or, in other words, the greater the 
magnetizing power — the greater will be the number of 
molecules which are thereby arranged into more or less 
complete magnetic chains, and if the metal is hard enough 
these chains in their turn become the seat and origin of 
lines of force, and can then be used to magnetize other 
bars. It will also be clear that after a bar has been 
magnetized, the space surrounding it becomes filled with 
lines of force which emanate from it. Strictly speaking, 
each magnet is surrounded by lines extending into in- 
finite space, but practically they can only be traced 
throughout the space immediately surrounding the mag- 
net, and this space is called the " magnetic field" Since 
magnetic lines are not a reality, but only a convenient 
conception, we can adopt any simple way of expressing 
their magnitude, or, to speak more correctly, the inten- 
sity of the magnetic field at any given point. We can 
either assume that the lines are of different strength, and 
that the mechanical force with which a given free magnet 
pole is urged along any one particular line is dependent 
on the strength of that line, which may be different from 
that of any other line belonging to the same field ; or we 
can assume that all the lines are of the same strength, but 
that the number of lines passing through unit space of the 
field is different at different points of it. According to this 
assumption, the intensity of the field in any given spot, 
and the mechanical force exerted on a free magnet pole, 
is proportional to the number of unit lines passing through 
unit space at that particular spot. This is the more con- 
venient way of estimating the magnitude of the mechanical 



32 ELECTRIC TRANS31ISSI0N OF ENERGY. 

forces produced by the magnetic field, but it must not be 
considered to be a representation geometrically true, and if 
we try to consider it so, the want of reality in our concep- 
tion of lines of force becomes at once apparent. This will 
be seen from the following consideration. If, as we assume, 
a mechanical force can only be exerted by lines actually 
passing through the magnet pole, it will be evident that 
in case the pole be a mathematical point, only one line 
can pass through it and exert mechanical force on it. 
This force would therefore be quite independent of the 
density of lines around the pole. If the pole, although 
of the same strength, had finite dimensions, more lines 
would actually pass through it, and more mechanical 
force would be exerted. Experiment, however, shows 
that this is not the case, and that within reasonable 
limits the mechanical force is independent of the extent 
of the pole, and only depends on its free magnetism. 
From this we conclude that a strictly geometrical repre- 
sentation of the density of lines in a magnetic field, in the 
same manner as we might represent the density of trees in 
a forest, would be incorrect. We cannot pretend to solve 
the problem of finding a geometrical representation for 
our conception of the intensity of the magnetic field, and 
we must be content to use the term in its conventional 
sense, without having any clear idea of how it could be 
represented by a mechanical model. Yet this is no reason 
why we should abandon such an extremely convenient 
method of representing magnetic action at a distance. 
Nobody has as yet succeeded in explaining the action 
of gravitation, or has been able to represent it by a 
mechanical model. Nevertheless we find no difficulty in 
using the conventional terms of acceleration, mass, and 
weight of bodies in our calculations. We know that the 



FUNDAMENTAL UNITS. 33 

weight of a body equals the product of its mass and the 
acceleration due to gravity. If we put strength of pole for 
mass and intensity of field for acceleration due to gravity, 
we find the analogue to weight in the mechanical force 
with which a free magnet pole is acted on when placed in 
a magnetic field. 

From what has been said above, it will be evident that 
we must define magnetic field of unit intensity as that in 
which a free magnet pole of unit strength is acted on 
with unit force. To define a magnet pole of unit strength 
we must have recourse to the well-known expression for 
the mechanical attraction or repulsion existing between 
two poles placed at a certain distance apart. The law 
has been established experimentally by Coulomb, 1 with 
the aid of his torsion balance, and verified by Gauss, 2 
who used for the purpose a large fixed magnet, and a 
smaller suspended magnetic needle. It is as follows. If 
M and m denote the strength of the two poles, and if they 
are placed at a distance, r, from each other, the mecha- 
nical force (attraction or repulsion according to whether 
the poles are of dissimilar or similar sign) acting between 

M m 

them is — ^- . If both poles are equal and of the strength 

717, 

m, we have —5-, and if their distance be unity, the force 
r 

acting between them will equal the square of the free 

magnetism of one pole. The force will be unity if the free 

magnetism is unity. We find, therefore, the definition 

for unit pole to be a pole of such strength that when placed 

at unit distance from an equal pole, the two will act upon 

each other with unit force. It remains to define unit force 

1 Wullner, " Experimentalphysik," iv. ? § 5. 

2 Wiedemann, " Elektricitat," Hi., p. 116, ante. 



34 ELECTRIC TRANSMISSION OF ENERGY. 

and unit distance. This might be done on any convenient 
basis of the measurements of mass, length, and time. In 
electrical calculations it is customary to use for this purpose 

The Gram as the unit of mass. 

The Centimeter as the unit of length. 

The Second as the unit of time. 

On these units is based what is known as the Absolute 
System of Electro- Magnetic Measurements. Taking these 
units as the basis for our calculations, we can find all 
other units of measurement, because they are all con- 
nected in some way with the fundamental units of mass, 
length, and time. We find thus that the unit of velocity 
in one centimeter per second, that of acceleration is an 
increase of velocity of one centimeter per second, and 
since mechanical forces are measured by the product of 
mass and acceleration, we define the unit of mechanical 
force, the Dyne, as that force which applied to a mass of 
one gram, during one second, will give it a velocity of (or 
accelerate its velocity by) one centimeter per second. 
The mechanical energy represented by the force of one 
dyne acting through a distance of one centimeter is the 
unit of energy, and is called the Erg. Having accepted 
these fundamental and derived units, we can now proceed 
to establish units for the lines of force, and for the inten- 
sity of the magnetic field. We call a unit line of force 
one of such strength that if a unit pole be placed on it, it 
shall be urged along it with the force of one dyne. A 
unit magnetic field would be one in which a unit pole 
would be acted on with the force of one dyne. If we find 
experimentally that an equal force is exerted in all points 
of a certain portion of the field (as is the case with the mag- 
netic field of the Earth within certain limits), we say that 
this particular portion of the field is of uniform magnetic 



ABSOLUTE MEASUREMENTS. 35 

intensity, and we consider all the lines of force to be 
straight, parallel, and equidistant. A uniform magnetic 
field of unit intensity is therefore one in which every square 
centimeter of transverse section is traversed at right angles 
by one unit line. We can now determine the number of 
unit lines which emanate from a free unit pole. Before 
doing so, a few words of explanation regarding this con- 
ception of a free magnet pole are necessary. It has been 
shown above that magnets are produced by the adjusting 
of their molecules into continuous chains ; and that, 
therefore, equal quantities of magnetic matter of opposite 
signs are produced at the poles of the magnet. Experi- 
ment shows that it is physically impossible to produce a 
magnet with one pole only, and that therefore no such 
thing as a free magnetic pole can be found in nature. 
But we can get an approximation to the free pole by 
making the magnet very long in comparison to the 
strength of its poles. In this way the magnetic influence 
of each pole will be sensibly felt through a distance con- 
siderably smaller than the length of the magnet, and 
when investigating the magnetic properties of the space 
immediately surrounding one pole we can neglect the dis- 
turbing influence of the other pole. In this case the 
lines of force emanating from the pole under consideration 
will be straight radii, shooting out from the pole all 
around into space. Let, in Fig. 4, Pbe the pole, and S 
a sphere described around it as centre, then this sphere 
will be pierced by the lines of force, in points which are all 
equidistant from the pole. Let r be that distance, and M 
the strength of the pole, we find the mechanical attraction 
exercised upon a unit pole of opposite sign placed at any 

M 

point on the surface of the sphere, by the expression — r 



36 ELECTRIC TRANSMISSION OF ENERGY. 

If, now, a second sphere be described around P, with a 
radius larger than r by only an infinitesimal amount, we 
shall have a spherical shell of infinitely small thickness, 
within which the intensity of the field is uniform. Into 
whatever point between the two surfaces of the shell we 
may place our unit pole, we find that it is attracted with 
the same force towards P, and from this we conclude that 
the density of lines all over the spherical surface must be 
uniform. Since in a uniform field the force exerted upon 
unit pole in the direction of the lines is equal to their 

Fig. 4. 



density (or number of lines per square centimeter of 
transverse section), we conclude that through each square 

M 

centimeter of surface on the sphere, there pass — unit 

lines. Now the total surface of a sphere of radius r, is 
4 7r r 2 , and consequently the total number of lines ema- 
nating from the pole of the strength M is 

2 M 

4:17 r X - 2 = 4 7T M 

r 

If the pole P, instead of having the strength M 9 were a 



ABSOLUTE MEASUREMENTS. 37 

unit pole, the total number of lines would evidently be 
4 ir, and thus we find a second definition for unit pole 
as a pole of such strength that 4 ir unit lines of force 
emanate from it. This definition is evidently identical 
with the following : Unit pole produces unit intensity of 
field at unit distance. 

Up to the present we have only dealt with magnets and 
the mechanical forces exerted by them. It will now be 
necessary to investigate the relations between an electric 
current and the mechanical force it can exert when 




brought into a magnetic field. Experimental facts form 
now, as before, the basis of our investigation. Let, in 
Fig. 5, a be the cross-section of a wire passing vertically 
through the surface of the paper, and assume that a 
current is flowing down the wire. If we sprinkle iron 
filings on to the paper near the wire, we find that they 
arrange themselves in concentric circles around it, and 
if we shift the paper into other places along the wire, we 
find the same result. From this experiment we conclude 
that the wire throughout its whole length is surrounded by 
circular lines of force, or as it is sometimes called, by a 
magnetic whirl. If we suspend a long thin magnet 
parallel to the wire, so that its lower end is free to move 
along the surface of the paper, it will have a tendency to 



38 ELECTRIC TRANSMISSION OF ENERGY. 

rotate round the wire, but continuous rotation cannot be 
obtained, because the upper end of the magnet has a 
tendency to circle round the wire in an opposite direction. 
If a short magnetic needle, suspended in its centre, is 
placed horizontally on the paper, it will set itself tan- 
gentially to the lines of force, and therefore at right 
angles to the wire. Each circle of iron filings must be 
considered as a chain of small magnets closed in itself, 
and if we were to lay a ring of steel around the wire on 
the paper, it would become a continuous magnet. Upon 
removing the ring it would not show any external mag- 
netization, because all along, its molecules are in contact 
with their opposite poles, but if we interrupt this con- 
tinuity by cutting the ring open in one place, the ends 
severed will show opposite polarity when the ring is 
straightened out. If, instead of a complete ring, we had 
placed only a segment of a ring or a straight piece of 
steel at right angles to the wire, it would upon removal 
at once show magnetic properties. We see from these 
experiments that it is possible to magnetize a piece of 
steel by passing an electric current in its neighbourhood 
at right angles to it. All the experiments detailed above 
will succeed equally well with a bent wire, and if we 
employ a coil of wire with a piece of steel inserted at 
right angles to the plane of the coil, its magnetization 
will be considerably greater than where only one straight 
wire is used. The annexed sketch, Fig. 6, will give a 
clear idea of the lines of force surrounding a circular coil 
in which a current flows. The zinc and copper plate of 
a voltaic cell are joined by a stout square wire bent into 
the form of a circle, as shown, and since all the lines pass 
around the wire in the same sense it follows that the whole 
interior space of the circle is filled by a bundle of lines 



ABSOLUTE MEASUREMENTS. 



39 



piercing the plane of the coil at a right angle. A free 
magnet pole would therefore be drawn through the coil 
in one sense or the other, according to the sign of the 
pole and the direction of the current. If a small magnetic 
needle be suspended in the centre, it will set itself at 
right angles to the plane of the circle and the direction in 
which its N pole is urged, is given by the following rule 
due to Ampere : Imagine a person sivimming with the 

Fig. 6. 




current and looking towards the needle, then its N pole will 
be urged towards the left. If, instead of a magnetic needle, 
we place a non-magnetic piece of steel into the same posi- 
tion it will become magnetized, .N at its left and S at 
its right end. It will be evident that if we approach 
the N pole of a magnet to the circle from the front, the 
side turned towards the observer in the figure, it will 
be repelled, and if we approach a S pole it will be at- 
tracted. The opposite takes place on the back. The 



40 ELECTRIC TRANSMISSION OF ENERGY. 

same would happen if instead of the circular wire tra- 
versed by a current, we had a very short magnet of equal 
diameter. To put the magnet into the same condition as 
the wire its length would have to be equal to the thick- 
ness of the wire, and it would thus become a flat disc, 
one side of which we assume to be covered with N mag- 
netic matter, and the other side with an equal amount of 
S magnetic matter. By properly choosing the amount 
of magnetism distributed over the discs, we can obtain a 
magnet which in its action at a distance is absolutely 
equivalent to the circular current, and such a magnet is 
called the equivalent magnetic shell. The action which a 
physical magnet or a magnetic shell equivalent to a 
closed current can exert at a distance is most conveniently 
expressed by the magnetic moment, that is the product of 
strength of poles with their distance. A magnet one 
centimeter long having unit poles has unit moment. 
Experiment shows that the magnetic moment of a plane 
closed circuit is equal to the product of area enclosed by 
the current and strength of the current, and we can 
therefore define unit current as that current which flowing 
in a plane circuit is equivalent to a magnetic shell the moment 
of which is numerically equal to the area of the circuit. Let 
in Fig. 7, a b represent the cross-section through a cir- 
cular conductor of radius, r, traversed by a current, c, 
and m, a magnet pole placed at a distance, d, from the 
centre of the coil, then it is found experimentally that 
each element of the conductor exerts a force on the 
magnet pole which is numerically equal to the product of 
strength of current by length of element, by strength of 
pole divided by the square of the distance ; and the direc- 
tion of which is at right angles to the plane passing 
through the element and through the magnet pole. The 



ABSOLUTE MEASUREMENTS. 41 

force due to the element, d 7, situate at ft, is therefore 



m 



C dl 771 

f, and its amount is d F = -^- -—■ The horizontal 



'■ + r 2 



component of this force is evidently d H = d F . , 2 - a 

and since the same holds good for any element along the 
circle, we find the total force by integration between the 

2irr 2 



limits o and 2 ir r H 

Fig. 7. 



c. m, 



(d 2 + r 2 ) 




If the magnet pole lies in the centre of the coil, d = o, 
and the force is evidently H = — — - — . 

This equation provides another definition for unit 
current. It will be seen that if m, r and c are equal to 
unity, H is equal to 2 7r, and we may define unit current 
as that current which, flowing i7i a wire forming a circle of 
unit radius, acts on a unit pole placed at the centre with a 
force of 2 it dynes. 

If a magnet be inserted into a coil of wire which is 
connected to a delicate galvanometer, a current will be 
observed to flow through it for a short time, and if the 
magnet be withdrawn from the coil, a momentary current 
in the reverse direction is created. Now since it is im- 
possible that a current should flow without there being 



42 ELECTRIC TRANSMISSION OF ENERGY. 

an electromotive force in the circuit, we conclude that 
the act of thrusting a magnet into the coil, or suddenly- 
withdrawing it, sets up an electromotive force in one direc- 
tion or the other in the wire itself. To explain this phe- 
nomenon, we have again recourse to the conception of 
lines of force. It is evident that in approaching the 
magnet to the coil we move not only the metal alone, but 
also all the lines of force which surround it, and in so doing 
we cause these lines, or at any rate some of them, to cut 
the wire of the coil. The same happens if the magnet 
remains at rest and we move the coil relatively to it ; the 
wire cuts through the lines of force and an electromotive 
force is set up in it in consequence. We cannot explain 
the why and wherefore of this action, and must rest con- 
tent to accept it as abundantly proved by experiment. 
A careful investigation also shows that the strength of 
the current, and consequently the amount of electro- 
motive force set up, is directly proportional to the speed of 
movement and to the strength of the magnet. We con- 
clude from this that the electromotive force is proportional 
to the rate of cutting lines, that is, to the number of lines 
cut per second by each wire. It is also proportional to 
the number of wires in the coil. We also find that in 
thrusting the magnet into the coil we experience a resis- 
tance necessitating the expenditure of mechanical energy, 
the amount of which is proportional to the product of cur- 
rent and electromotive force. This resistance, and the 
mechanical energy necessary to overcome it, will be the 
greater the lower the electrical resistance of the coil, pro- 
vided other things remain equal, and if the coil be open 
so that no current can pass, there will be no opposing 
force to the movement of the magnet. In order to inves- 
tigate this phenomenon of the creation of electromotive 



POTENTIAL. 43 

force by the movement of a conductor in a magnetic field, 
we will assume the simplest possible case, viz., that of a 
uniform field, the lines of which we suppose to be vertical. 
Let two metallic bars be fixed at equal distance from the 
ground, and parallel to each other, and let a third bar, 
which we term a slider, be laid at right angles across these 
bars, and let it be free to move parallel to itself, but al- 
ways remaining in contact with them. As soon as the 
slider is set in motion, a difference of potential will be 
created between its ends where it rests on the bars, tend- 
ing to make electricity flow from the bar of higher to the 
bar of lower potential. Such a flow of electricity will 
actually take place, and can be made visible if the bars 
be connected by a galvanometer. Let d be the distance 
between the bars, v the velocity of the slider, and F the 
intensity of the field, then the difference of potential be- 
tween the bars, is F. d. v, which product also expresses 
the number of lines of force cut by the slider per second. 
If the distance between the bars be one centimeter, and 
the velocity one centimeter per second, and the intensity 
of the field be also unity, we obtain the unit of electro- 
motive force. We define, therefore, as the unit of electro- 
motive force, that which is created in a conductor moving 
through a magnetic field at such a rate as to cut one unit 
line per second. Imagine that the bars and the galvono- 
meter connecting them have absolutely no electrical re- 
sistance, but that the slider has a resistance r, then by 
Ohm's law the current produced through the circuit, 
whilst the slider is in motion, will be 

F. d. v 

c = . 

r 

If the intensity of the field is unity (F = 1), and if the 

bars are one centimeter apart, unit current will be pro- 



44 ELECTRIC TRANS3IISSI0N OF ENERGY. 

duced at a velocity v = r. We find, therefore, that the 
electrical resistance of the slider, and for the matter of 
that the electrical resistance of any conductor, can be ex- 
pressed in the same terms as a velocity. We say that the 
resistance of a conductor is so many centimeters a second. 
It is customary to express resistances by reference to a 
standard resistance, the ohm. The relation between this 
and the unit of resistance in absolute measure will be 
shown presently. Before doing so, we must, however, 
say a few words about the energy required to move the 
slider, and about the relation between current and mecha- 
nical force. Let P represent the pull in dynes required 
to move the slider across the lines of a field of intensity 
jF, with a velocity of v centimeters a second. The energy 
expended in ergs will evidently be 

W=P.v. 
By the principle of the conservation of energy, this must 
be equal to the electrical energy produced. The ques- 
tion which now presents itself is the determination of the 
electrical energy of a current, c, flowing under a difference 
of potential of F. d. v. We have up to the present used 
the term potential without giving its definition. As the 
name implies, the potential of a body is its property of 
allowing energy stored up in it to become potent, that is, 
to do work. If a weight be raised to a certain height 
from any given datum level, the mechanical work thereby 
expended can be recovered by allowing the weight to 
descend again whilst overcoming the resistance of some 
piece of mechanism which can be made to do useful work. 
In its elevated position the weight has, therefore, a cer- 
tain potential energy, which is equal to the product of 
the weight multiplied by the distance to which it has 
been raised. If the weight be unity, this product is 



CURRENT AND MECHANICAL FORCE. 45 

numerically equal to the height, and we can say that the 
mechanical potential of a heavy body raised to a certain 
height above datum level equals the mechanical energy 
required to lift unit weight to the same height. By 
multiplying the potential thus defined with the weight 
of the body we obtain the total mechanical energy which 
it is capable of exerting. Similar reasoning applies with 
regard to the transfer of electricity. It is well known 
that two bodies charged with electricity of the same sign 
repel each other, and if one of the bodies is fixed whilst 
the other is being approached to it mechanical energy 
must be expended in the act of approaching. This energy 
can again be recovered (provided there were no losses by 
dissipation of electricity into the surrounding air) by 
allowing the movable body to recede from the body at 
rest whilst doing useful work. To fix ideas, let the 
stationary body be a very large metallic sphere charged 
with a certain amount of positive electricity, and let the 
movable body be a very small gilded pith ball charged 
with a unit of positive electricity. We assume a great 
difference in the size of these bodies in order that the 
charge on the larger body shall not be sensibly altered 
by the variation of position of the small body. If we 
remove our pith ball to an infinite distance, so as to be 
completely beyond the repulsive action of the larger 
body, we can consider it to be in that position analogous 
to unit weight placed at datum level. If we now advance 
the pith ball up to the large sphere, we shall have 
to perform mechanical work, and, according to Lord 
Kelvin's definition, the electrical potential of the sphere 
is measured by the amount of mechanical work per- 
formed. If, instead of starting from infinite distance, 
we had started from another sphere having a different 



46 ELECTRIC TRANSMISSION OF ENERGY. 

potential from the first, the mechanical work performed in 
the transfer of the pith ball would be a measure of the 
difference of potential between the two spheres. It will 
appear self-evident that if, instead of only one pith ball, 
we transfer two, three, or more, or if the charge of the 
pith ball, instead of one unit, were two, three, or more 
units of electricity, the mechanical energy would also be 
increased in the same proportion. From this it follows 
that the mechanical energy required to transfer q units 
of electricity from a sphere or point where the potential 
is pi to a sphere or point where the potential is p 2 will 
be— 

— qiPi—p*) 

and this result will not be altered if the transfer, instead 

of taking place by the aid of our pith ball conveying a 

definite electrical charge q, were to take place by means 

of a wire carrying a continuous current, since the latter 

can be considered as a succession of pith balls. In our 

experiment with the slider, c is the current or quantity of 

electricity transferred in one second, and the mechanical 

energy represented by the current during the interval ot 

one second is therefore 

c F d v, 

which by the principle of the conservation of energy 

must be equal to the mechanical energy expended during 

one second in moving the slider. We find, therefore, the 

relation 

P= c Fd. 

The mechanical force experienced by a straight conductor 
d centimeters long, carrying a current c, and situate in a 
uniform field of intensity F, the lines of which are at right 
angles to the conductor, is equal to the product of length of 
conductor^ current, and intensity of field. This relation is 



IDEAL MOTOR. 47 

of the utmost importance for the construction of electro- 
motors, inasmuch as the mechanical forces thus deter- 
mined are the real source of power of these machines. It 
would, therefore, be desirable to verify the expression 
obtained above by some other method of reasoning, and 
this can easily be done if we go back to what has been 
said about the relation existing between a current and 
the force exerted by it on a free magnet pole. It was 
then stated that experiments have shown the force to be 
equal to the product of length of conductor, current, and 
strength of pole, divided by the square of the distance. 
We assume hereby that the conductor stand at right 
angles to the line joining its centre with the pole, and 
that it be very small in comparison to the distance from 
the pole. All the straight lines which can then be drawn 
from the pole to different points of the conductor inter- 
sect it at right angles, and can be considered to be 
parallel. The conductor lies, therefore, in a uniform 

Vfl 

magnetic field of the intensity F = ~ 2 , m being the 

magnetism of the free pole, and R its distance from the 
conductor. Let d be the length of the conductor, c the 
current, and P the mechanical force exerted on the pole, 
we have 

__ m c d 

as has already been shown. But since action and reaction 
must be equal, the conductor acts upon the pole with pre- 
cisely the same force as that exerted by the pole on the 
conductor ; and we find that the force tending to lift the 
conductor out of the plane laid through it and the pole 

is also equal to P. By substituting F for -^ we have 



48 ELECTRIC TRANSMISSION OF ENERGY. 

therefore P = c F d, the same expression as obtained 
above. 

Returning now to the above example of the two hori- 
zontal bars and the slider laid across them, let, in Fig. 8, 
A B, C D, represent the two bars, a b the slider, and V 
a voltaic cell connected to the bars by wires, as shown. 
The lines of force — not shown in the diagram — are sup- 
posed to be vertical, and therefore at right angles to the 
slider and to the bars. From what has been stated above, 
it will be seen that on establishing connection with the 
voltaic cell, the current flowing through the slider will 




generate a force tending to move it along the bars 
parallel to itself. This force could be utilized by attach- 
ing a cord to the slider, which, passing over a pulley, 
could be made to raise a weight. We have here the 
most simple case of transforming electrical into me- 
chanical energy. As soon as the slider begins to move, 
it cuts through lines of force, and, as was explained 
above, by this action a difference of potential is created 
at its ends, or, as we can also express it, the slider be- 
comes the seat of an electro-motive force. A moment's 
reflection will show that this electro-motive force must be 
directed in opposition to the electro-motive force of the 
cell, for, were it not so, the original current would be in- 



IDEAL MOTOR. 49 

creased by the creation of this second electro-motive force, 
and we should thus obtain additional electrical energy 
and mechanical energy at the same time, which is clearly 
incompatible with the principle of the conservation of 
energy. If in a circuit there are two electro-motive 
forces, the current resulting from their combined action 
is proportional to their sum. Since, in this instance, the 
electro-motive force of the slider is opposed to that of the 
cell, we must consider it to be negative, in fact a counter- 
electro-motive force, and the resultant electro-motive force 
in the circuit will be E — e, if by E we denote that of the 
cell and by e that of the slider. The resultant current 
is therefore found by dividing E — e by the total resistance 
of the circuit. As the slider moves along the bars, this 
resistance is evidently constantly increasing or diminish- 
ing, according to the direction in which movement takes 
place. Not to complicate the problem by the introduction 
of a variable resistance, we shall therefore assume that 
the bars are so thick as to have practically no resistance, 
and in that case the total resistance will consist only of 

that of the slider, the connecting wires, and the cell. Let 

E e 

that be r as before, and we find the current c = by 

Ohm's law. 

The mechanical energy exerted in raising the weight 
P with a velocity of v is per second : W ' = Pv ; and that 
must be equal to the electrical energy which is the pro- 
duct of current and difference of potential between the 
ends of the slider. Let, as before, F represent the inten- 
sity of the field, and d the length of the slider, we have : 
W=cFdv 

W=*^Fdv, 
r 

E 



50 ELECTRIC TRANSMISSION OF ENERGY. 

and since e = F d v, we have also 

W = F d v. 

r 

According to our former definition of intensity of field, F 
represents the number of unit lines of force passing 
through one square centimeter of surface between the 
bars, and d v is the surface swept over by the slider in 
one second. The product F d v represents, therefore, the 
number of unit lines cut by the slider per second. If we 
denote this number by z s we have also the following ex- 
pression for the mechanical energy represented by the 
raising of the weight : 

JV=z z. 

r 

This formula will be used later on for the determination 
of the mechanical energy obtainable with a given electro- 
motor. For the present it will be more convenient to 
retain the symbol e, and we write, 

r 

Since e = F d v, and P = c F d, we have the relation, 

p= c A 

v 
from which it will be seen that with a constant speed 
and with a constant current the weight which the slider 
is capable of hauling up, and therefore its capacity of 
doing work, is directly proportional to the counter-electro- 
motive force. It will also be seen how mistaken is the 
notion that counter-electro-motive force in an electro- 
motor is a loss, and that those well-meaning but confused 
inventors who strive to design motors which shall have as 
little counter-electro-motive force as possible, so as not to 



IDEAL MOTOR. 51 

check the flow of current which works the motor, would, 
if they were successful, obtain machines which could not 
give out any power at all. 

The energy given out by the cell is E c, that performed 
by the slider is e c, and the efficiency of our simple motor 
is therefore 

e 
n= E' 

In order to find the condition of maximum work per- 
formed, we form the differential quotient of W y and equal 
it to zero, the variable being the counter-electro-motive 
force e. That gives, 

dW„ d 



o 



= E ~ e + e TT (E-e), 



d e ~ ^ 
o = E — 2 e, 
E 



If the speed of the slider be so regulated, by adjusting 
the load, that its counter-electro-motive force is equal to 
half the electro-motive force of the cell, the maximum 
possible amount of mechanical work will be performed, 
the efficiency in this case being 50 per cent. 



W max. = £ — , 



In order to obtain that speed of the slider, we must regu- 
late the weight P attached to the cord, so that, 
m _ E EFd E 

V ~ 2-F~d> P = ~Tr> and C = 2r 
If a heavier weight were attached to the cord, the 
current would be greater and the speed smaller ; if a 
lighter weight were attached, the current would be less 
and the speed greater. In both directions there exists a 



52 ELECTRIC TRANSMISSION OF ENERGY. 

limit which will be reached, on the one hand by reducing 
the weight to zero, when the speed will be a maximum, 
and, on the other hand, by using so heavy a weight that 
the slider cannot move at all, when the current will be a 
maximum. These limiting values can easily be obtained 
from the above formulas, and are as follows : 

Weight completely removed, 

E 

P = o, c = 0, e — E, v = r=---. 

Weight just balances force of slider, which remains at 

rest, 

n E F d E 

F = 3 c = — 9 e ~ o, v =z o. 

r r 

On comparing these expressions with those found for the 
condition of maximum work, it will be seen that in the 
latter case the current is half as great as that obtained 
with the slider at rest, and the velocity half as great as 
that of the slider with the weight removed. The statical 
pull on the slider when doing maximum work is half that 
obtained with the slider at rest. 

These investigations, although at first sight they might 
seem somewhat abstruse, becaase no engineer would think 
of pulling up weights by the arrangement of a slider as 
described, are nevertheless of great practical importance. 
Imagine that, instead of having a single slider, we place 
a number of wires on the surface of the armature of an 
electro-motor, and that we arrange to have a very intense 
field by the employment of steel or electro-magnets with 
suitable devices for commutating the current in the arma- 
ture wires, which enable us to transform the rectilinear 
motion of the slider into a continuous rotary motion ; and 
we obtain at once an eminently practical machine. This 
machine does not differ in principle from our simple slider, 



IDEAL SYSTEM OF TRANSMISSION. 53 

and all the general laws we have found above for the 
latter are therefore applicable to the former. Certain 
allowances will, of course, have to be made on account 
of the usual mechanical resistances and losses common to 
all mechanism, and also on account of certain secondary 
actions and electrical losses or imperfections inseparable 
from the adaptation of an abstract or ideal machine to 
actual work ; but, in general, the laws deduced above 
hold good in practice. Thus we shall find, that if an 
electro-motor, having permanent field magnets (either of 
steel, or electro-magnets excited by a constant current), 
runs at a speed of 1,000 revolutions a minute when doing 
no external work, whilst supplied with current at a given 
electro-motive force, it will do a maximum of work when 
loaded to such an extent that its speed drops to about 
500 revolutions a minute, the electro-motive force re- 
maining the same. If loaded more and more, say by the 
application of a brake, the speed will be further reduced 
until the armature of the motor comes to a standstill. In 
this condition, the statical moment of the armature, or the 
torque as it is also called, will be twice as great as when 
running at 500 revolutions, and the current passing 
through it will also be twice its former value. This fact 
is of importance, as it enables us to calculate the starting 
power of the motor, a point of great interest in the appli- 
cation of motors to tramway or railway carriages. We 
must at once observe that so large a current should never 
be allowed to pass through the armature for more than a 
very few seconds ; and when in regular work, motors are 
generally so loaded as to run faster than half their idle 
speed, partly because the current corresponding to half- 
speed would still be excessive, and heat the wires too 
much, and partly because we are, as a rule, not content 



54 ELECTRIC TRANSMISSION OF ENERGY. 

with so low an efficiency as 50 per cent. From the 
formula for the efficiency given above, it will be seen 
that the nearer the counter-electro-motive force ap- 
proaches to the electro-motive force of the source of 
current (a voltaic cell in our example), the nearer does 
the coefficient of efficiency approach to unity. But to 
obtain a high counter-electro-motive force we must allow 
the motor to run at a high speed. 

It has already been shown how a slider, when moved 
across the lines of a magnetic field over two metallic bars, 
can be made to produce a current in a wire joining the 
two bars. It has also been shown how a current sent 
from an external source into the bars, and through the 

Fig. 9. 



A 


/ 


/ 


B 


— ^-jL. jl j. j ^ *- 


^7 


? B- 




/ 

a 


Z> s 




£>■ 



slider, will cause the latter to move and perform mecha- 
nical work. Let, in Fig. 9, A B, C D, be the bars 
receiving the current, and A Y B l9 C x D i9 be the bars in 
which the current is originated by the movement of the 
slider a Y b l9 and it will be clear that by performing 
mechanical work on the latter slider, we can cause the 
slider a b to give out mechanical work by raising a 
weight, as explained above. We have here the most 
simple possible case of the electric transmission of 
energy. The generating system, A Y B 1} C v Z>„ can be at 
any distance from the receiving system, A B, C Z>, and 
all that is required are electrical connections (wires to 
carry the current) between ^and B, and between C x and 
D. Let the intensity of the magnetic field be F v at the 



EFFICIENCY. 55 

generator and F at the receiver, and let the pull applied 
at the generating slider be P l9 whilst that exerted by the 
receiving slider is P ; let also v x and v be respectively 
their velocities, and e\ and e respectively the electro- 
motive forces, then the following equations evidently 
obtain : 







c- e > 


r 


e 

9 


«1 


= 


F 1 d x v l9 






€ 


= 


F dv, 







F 1 d l v 1 — Fdv 
F 1 = F x d ly 

p _ F l d l v x — Fdv Fd 

r ' 

P ~ F d' 
This equation shows that the pull exerted on the gene- 
rating slider, and that given out on the receiving slider, 
bear a fixed proportion to each other which is indepen- 
dent of the speed, but depends on the intensities of the 
fields and on the dimensions d x d of the sliders. The 
energy expended at the generating system is 

and that given out by the receiving system is 

us -n j F l d l v v — F d v 

fV= F d v — — - — 

r 

The ratio between the two, or the efficiency of transmission, 
is evidently 

F d v 

F x d x v L 
If both systems are identical as regards dimensions and 



56 ELECTRIC TRANSMISSION OF ENERGY. 

V 

strength of field, y\ = — . This would be the case where 

two identical dynamos are employed, the one as receiver 
and the other as motor, both machines being series 
wound, so that the same current circulates around both 
sets of field magnets. In such cases it has been custo- 
mary to determine the electrical efficiency of the trans- 
mission of energy by simply determining the speeds, and 
taking their ratio. If no losses and no secondary actions 
would occur in the connecting wires and in the machines, 
no objection could be raised to this way of determining 
the efficiency; but in practice there are some very 
serious objections to this method. In the first place, the 
two magnetic fields, although produced by the same 
magnetizing power, are not of absolutely equal intensity, 
because the magnetization of the armature produced by 
the current circulating through its coils has a certain in- 
fluence in altering the intensity of the magnetic field, and 
this alteration is different in a motor from what it is in a 
dynamo. In the second place — and this is a fatal objec- 
tion — any leak or loss of current taking place at some in- 
termediate point in the wires by which th§ machines are 
connected, instead of lowering the efficiency, as deter- 
mined by the speeds, has actually the effect of making it 
appear higher than it really is. This will become obvious 
by reference to the equation for the counter-electro-mo- 
tive force of the receiving machine. Since e = Fd v, any 
reduction in F, consequent upon the loss of some of the 
magnetizing current through a leak in the line, has 
naturally the effect of increasing v, the velocity of the 
receiving machine, and thus it may happen that through 
the development of a fault in the insulation of the fine 
the ratio of speeds will increase, thus showing apparently 



LOST ENERGY. 57 

an increase of efficiency, whereas in reality the system 
has become less efficient. The variables in the above 
equations are v } v l9 P, and P v ; the dimensions of the 
machines (or sliders) d and d l9 and the intensities of the 
fields being constant. Since the ratio between the static 
efforts, P and P l9 is also a constant, the number of 
variables is reduced to three, and, if two of these are 
given, the third can be found. As an example, we will 
take the case that the load P to be put on the receiving 
machine shall be given (say, for instance, the pull re- 
quired to haul up a train on a steep gradient, but neglect- 
ing for the moment the difference in pull caused by varia- 
tions of speed) and the speed v x of the generating machine 
shall also be given. We require to know the power neces- 
sary to drive the generating machine, and the speed and 
energy developed by the receiving machine. From the 
equation for P, we find immediately the speed of the 

receiving machine, 

F x d x r P 

V ~~ Vl F d F 2 d 2 ' 
As will be seen, this speed is not directly proportional to 
the speed of the generator, and if the latter be increased 
the speed of the receiver will increase in a somewhat 
faster ratio. Since the ratio of -speeds enters into the 
formula for the efficiency, it will be evidently advanta- 
geous to work the machines at the highest possible speed 
consistent with mechanical safety. On the other hand, if 
we lower the speed of the generator beyond a certain 
point the receiver will not be set in motion at all. 

This will happen if v x j~ = -pr#i> 

r P 

v = 



FdF, d{ 



58 ELECTRIC TRANSMISSION OF ENERGY. 

In this case the efficiency is zero. The minimum speed 

of the generator is therefore dependent on the dimensions 

of the two machines and on the strength of the two fields, 

and is inversely proportional to the product of these four 

quantities. 

The mechanical energy which has to be applied to the 

x'i d* 
generator is W x = Pv l -r= r —= 9 

and that obtained from the receiver is 

the difference between the two being lost. This loss, 

which is represented by the expression r I - 1 , 

we must regard as energy transformed in a way not suit- 
able for the purpose in view. Since it does not appear in 
the shape of mechanical energy we must expect to find it 
appearing in the shape of heat, and this is indeed the 
case, as can easily be proved. It has been pointed out 
above that the static pull is the product of current, field- 
intensity, and the dimension of the machine. The 

P 

quotient —rrj represents, therefore, nothing else but the 

current flowing through the circuit, and the above term 
for the energy lost can also be written in the form 

r c 2 , 
which, as is well known, represents the heat developed 
by the passage of the current c through a circuit, the 
electrical resistance of which is r. Thus the whole of the 
energy applied at the generator is accounted for, partly 
by that given out by the receiver, and partly by that 
used up in heating the circuit. It need hardly be men- 
tioned that the formulas given here for the transmission 



PRACTICAL UNITS. 59 

of energy refer to ideal machines which are free from all 
other losses, both mechanical and electrical, but that in 
actual practice these other losses cannot be neglected, 
and considerably complicate the problems to be solved. 
The author, nevertheless, has thought it advisable to 
enter at some detail into the case of transmission of 
energy by means of ideal machines, not because the 
formulas obtained are immediately applicable to practical 
cases, but because they form the basis of other formulas 
suitably altered for practical purposes, and which will 
be given in a subsequent chapter. The example cited is 
also intended to show how easily and simply the system 
of absolute electro-magnetic measurement can be applied 
to apparently complicated problems. Before leaving this 
subject we must refer to the relation between electrical 
units in absolute measure and those units commonly 
used in practice. The units as given in the centimeter- 
gram-second system are of inconvenient magnitude for 
practical purposes ; some of them are so small that 
millions and even larger figures are required to express 
quantities commonly dealt with in practical work, and 
others are, again, so large as to necessitate the use of 
fractions. We had already occasion to refer to the three 
units most often occurring in electro-mechanical pro- 
blems, viz., current, electro-motive force, and resistance. 
The unit of quantity of electricity has also incidentally 
been mentioned as represented by that amount of elec- 
trical matter which a given current conveys in one second. 
For the sake of completing the list we must also mention 
a property of conductors called their capacity, by which 
term we mean their capacity or power to hold an elec- 
trical charge. The capacity is measured by the quantity 
of electricity with which a body can be charged under an 



60 



ELECTRIC TRANSMISSION OF ENERGY. 



electro-motive force equal to unity. The relation between 
the so-called practical units and their equivalents in the 
centimeter-gram-second system is as follows : — 

Name of Electrical Quantity. 

Current strength . 
Electro-motive force 
Resistance 
Quantity of electricity 

Capacity 

Kate of doing work 



Practical Unit. 


Equivalent c. g. s 






Unit. 


Ampere * 




IO 1 


Volt. 




10 s 


Ohm 




IO 9 


Coulomb . 




io- 1 


f Farad 

( Microfarad 




io- 9 




io- 15 


Watt 


• 


10 T 



CHAPTEE II. 

First Electro-motor — Professor Forbes' Dynamo—Ideal Alternating Cur- 
rent Dynamo — Ideal Continuous Current Dynamo — Siemens' Shuttle- 
Wound Armature — Effect of Self-Induction — Experiments with Electro- 
motors — Hefner- Alteneck Armature — Gramme Armature — Pacinotti 
Armature — Electro-motive Force created in any armature. 

In the preceding chapter it was shown how mechanical 
energy can be converted into that of an electric cur- 
rent, and how the electric energy represented by a cur- 
rent flowing under a given difference of potential can be 
reconverted again into mechanical energy and do useful 
work. The apparatus employed for this double conver- 
sion was assumed to be of extremely simple form, in order 
to limit our investigation to the fundamental laws with- 
out obscuring these laws by the introduction of secondary 
actions and losses. It will now be necessary to confront 
the subject from a somewhat more practical standpoint, 
and to show how the conversion between mechanical and 
electrical energy can be obtained with machinery of a 
practical form. As a first step towards a practical 
solution of the problem to produce motive power by an 
electric current, we must consider Barlow's wheel, 1 in- 
vented by Sturgeon and Barlow about seventy years 
ago. A star-shaped wheel was mounted on a horizontal 
axis and set over a trough containing mercury in such 

1 Barlow, " On Magnetic Attraction." London, 1823. 



62 



ELECTRIC TRANSMISSION OF ENERGY. 



way that during rotation of the wheel one or two spokes 
were always dipping into the mercury. Fig. 10. A per- 
manent steel magnet N S was placed in such position 
that the lines of force joining its two poles passed trans- 
versely across the plane of rotation of the wheel, and upon 
sending a current through the wheel in the direction in- 
dicated by the arrows, rotation was produced in the oppo- 
site sense to the hands of a watch as seen from the side 
on which was placed the N pole of the magnet. It will 
be seen at a glance that this apparatus is nothing else 
but our arrangement of a slider in rotary form, the lines 

Fig. 10. 




of the magnetic field being in this case horizontal where 
they cut through the wheel. Each spoke is a slider 
coming successively into action as its extremity touches 
the mercury in the trough and is thus put in electrical 
connection with the rest of the circuit. It was also found 
that the experiment succeeded if, instead of a star wheel, 
a plain metallic disc was employed, the lowest point of 
the circumference just touching the mercury. In 1831 
Faraday reversed the experiment and obtained an 
electric current from a disc rotating between the poles of 
a magnet. Fig. 11. The magnet was so placed that the 
induction between the poles, that is, the lines of force 
passing from one pole to the other, should pierce the 



FORBES' NON-POLAR DYNAMO. 63 

surface of the disc, and the current was taken off by 
contact springs on the axis and on the circumference ; 
the latter being placed on the radius of greatest induc- 
tion. Lately Professor George Forbes has constructed 
dynamos on the same principle, the only difference being 
that, instead of using a permanent steel magnet, he uses 
an electro-magnet which becomes excited by the current 
produced. Professor Forbes' machine l is remarkable for 
the very powerful current it produces as compared to its 
small size. He has devised several modifications, but 

Fig. 11. 



"»-*-*> 




for our purpose it will be sufficient to describe one of his 
arrangements. The armature of this dynamo, which is 
illustrated in Fig. 12 in longitudinal section, consists of a 
wrought iron cylinder without any wire on it. The field 
magnet is a closed iron casing surrounding the armature 
on all sides, and containing two circular grooves of taper- 
ing section into which are laid the exciting coils E, 
formed of insulated copper wire. If a current passes 
through these coils, it produces lines of force which com- 
pletely surround each coil, and which pass partly through 
the iron shell C D forming the field magnet, and partly 
through the armature A. The general character of 
these lines is shown by the dotted curves. It will be seen 
that as the armature cylinder revolves it becomes the 

* See " The Engineer" of July 17, 1885. The author is indebted to the 
editor of that paper for the use of the engraving. 



64 



ELECTRIC TRANSMISSION OF ENERGY. 



seat of electro-motive forces acting at right angles to the 
lines, as indicated by the arrows, and if we provide rub- 
bing contacts at the ends of the cylinder we can obtain 
the current due to these electro-motive forces. The 
contacts are arranged at the inner periphery of the 
exciting coils, and consist of a series of carbon blocks 

Fig. 12. 




FORBES NON-POLAR DYNAMO. 



held in two copper rings, which are connected to the two 
terminal plates G G. The current is thus taken off all 
around the armature, and the latter contains absolutely 
idle portion. This is one of the reasons why the 



no 



machines are so powerful as compared to their size. The 
other reason is that the intensity of the magnetic field is 
very great. As will be shown in a subsequent chapter, 
when the theory of continuous current motors will be 



FORBES' NON-POLAR DYNAMO. 65 

given, the intensity of the magnetic field is the greater 
the smaller the clearance between the polar surface of the 
magnet and the core of the armature. In motors or 
dynamos, which contain copper wire coiled over the 
armature core, this clearance is necessarily greater than 
in Professor Forbes' dynamo, where the space between 
armature and magnet is just sufficient to allow of free 
rotation. The following figures will serve to give an idea 
of the relation between the size of these machines and 
their output of electrical energy. A dynamo having an 
armature six inches in diameter and nine inches in length, 
will, when driven at a speed of 2,000 revolutions a minute, 
give a current of 5,000 Amperes at a difference of poten- 
tial of two Volts. According to the inventor, an arma- 
ture four feet in diameter by four feet in length would 
produce an electro-motive force of sixty Volts when 
driven at a speed of 1,000 revolutions a minute. If we 
were to allow the current to increase in the same propor- 
tion as the area of the armature cylinder, this machine 
could produce 320,000 Amperes, and would require about 
30,000 h.-p. to drive it. This heavy current would, how- 
ever, generate more heat in the metal of the armature than 
could be dissipated at a moderate temperature, and the em- 
ployment of such an enormous power at the high speed of 
1,000 revolutions is of course out of the question, but on 
purely theoretical grounds it is interesting to notice how 
easily our simple experiment of the slider when suitably 
arranged in rotary form will lead to results which on ac- 
count of their magnitude are quite beyond the capability 
of modern engineering. Dynamos similar to that just de- 
scribed are generally called Uni-polar Dynamos. Pro- 
fessor Forbes prefers the title Non-polar Dynamos, and 
with good reason, for, as was pointed out already in the 

F 



66 ELECTRIC TRANSMISSION OF ENERGY. 

first chapter, a magnet with only one pole is a physical 
impossibility. All the dynamos of this class have the 
disadvantage of requiring to be driven at a very high 
speed in comparison with the electro-motive force they can 
produce. The reason lies in this, that the length of con- 
ductor cutting through the field is limited by the size of 
the armature. These machines are practically nothing 
else but dynamos having only one turn of wire wound 
on their armature core. An ideal machine of this kind is 
shown in Fig. 13. The field magnets A r S are placed 

Fig. 13. 




IDEAL ALTERNATING CURRENT DYNAMO. 

horizontally opposite each other, and their polar surfaces 
are bored out to form a cylindrical cavity within which 
one single turn of wire can be revolved by means of a 
crank. One end of the wire is joined to the axis A A, 
and the other to a metal sleeve M, rubbing contact 
springs B x B. 2 being arranged in order to take the cur- 
rent off the sleeve and axis respectively. The lines of 
force pass horizontally across the cylindrical cavity from 
N to S 9 and those which are contained within the space 
swept by the wire are cut twice during each revolution. 
The effect is the same as if we had attached our slider to 



IDEAL ALTERNATING CURRENT DYNAMO. 67 

a crank and by turning the latter had caused the slider to 
assume a reciprocating motion across the lines of the 
field. In that case, when the crank is vertical, that is, 
parallel to the lines of the fields the speed of the slider is 
a maximum, and therefore its electro-motive force is also 
a maximum. As the crank approaches either of its dead 
points, where it is horizontal, the speed of the slider and 
its electro-motive force diminishes and becomes zero at 
the moment the motion is reversed. From what was said 
in the preceding chapter, it will also be seen that the 
direction in which the electro-motive force acts depends 
on the direction of motion, and the current produced must 
therefore be alternating. If we plot the angles of the 
crank on the horizontal, starting from any given position, 
say, for instance, from its position at the end of the 
stroke, and the electro-motive forces on the vertical, we 
obtain a graphic representation of the relation between 
these two quantities. In a uniform field, where the 
electro-motive force depends only on the speed of the 
slider, but not on its position in the field, the electro- 
motive force is evidently proportional to the sine of the 
angle of the crank, and is given by the expression 

E = F d o) sin a, 
where w is the circumferential speed of the crank, and a, its 
angular position, the othersymbols beingthesame as before. 
It will be seen that E = 0, for a. = and <x = tt 9 whilst for 

a = - or a — — -, E attains its greatest numerical value, 

being positive or negative according to the sign of the 
angle. The same relations obtain in the ideal alternating 
current dynamo, Fig. 13. If the crank is in the position 
shown, the wire is in the middle of the S pole piece and 
cuts the lines of force at maximum speed ; if the crank is 



68 ELECTRIC TRANSMISSION OF ENERGY. 

vertical, the wire moves parallel to the lines, and its rate 
of cutting lines is zero. This position corresponds to the 
end of the stroke with an oscillating slider. When the 
crank is again horizontal, but pointing to the left, the 
wire is in the middle of the N pole piece, and again its 
speed across the lines, or its rate of cutting lines, and the 
electro-motive force are maxima, but the current will 
be in an opposite direction to what it was at first. If the 
crank be turned in the direction indicated by the arrow, 
the current will leave the machine at the contact spring 
B x during the time the crank is on the right-hand side of 
the vertical diameter, and it will flow from B 2 through 
the external circuit, and enter the machine at B l during 
the time the crank is on the left-hand side of the vertical 
diameter. Let n be the number of revolutions per 

71 

minute, then — 2 tt r == a, the circumferential speed of 

the wire, and the maximum of electro-motive force, irre- 
spective of sign is evidently 

JE= Fd ~ 2ttv. 
50 

Now 2 r d is the total space swept by the wire, and 
F 2 r d is the total number of lines passing through that 
space ; let z be that number, and we find for the maxi- 
mum of electro-motive force the expression, 

*V*ik ; x 

During one half revolution the electro-motive force in- 
creases from zero to this maximum, and then decreases 
again to zero. As far as practical applications of the 
dynamo are concerned, it is not the maximum electro-mo- 
tive force which we require to know, but the mean electro- 
motive force, which acting during the same time as the 



MAXIMUM ELECTRO-MOTIVE FORCE. 69 

variable electro-motive force, would cause the same quantity 

of electricity to flow through the circuit. Let, at any given 

moment, the wire occupy a position defined by the angle 

a from the vertical, and let it advance through an angle 

J a during the time £ t, then the quantity of electricity 

flowing through the whole circuit of resistance R is 

evidently 

^ F d co sin <z $ t 

** = iT ' 

a . 5 as N F d r . „ 

and since co = r ^— . m m . o q =■ — =— sin <z d a. 
o t M 

During one half revolution a increases from zero to tt, and 
the integral of the above expression taken between these 
limits gives 

o F d r 

The time occupied in this transfer of q units of electricity 

is t = — -, and if, during that time, a constant electro- 

co 

motive force E l were acting, the quantity transferred 
would be -^ . If this quantity is equal to q, we con- 
sider E l the average electro-motive force, and its value 
is given by the equation 

F l = - F d co. 

Since Fdcois the maximum electro-motive force generated 
at the moment when the wire is cutting the lines of the 
field at right angles, we have also 

F l =-F. 

fl- 
it should be noted that the mean value of F M F as here 
defined refers to the total quantity of electricity which 



70 ELECTRIC TRANSMISSION OF ENERGY. 

the apparatus is capable of forcing through a given re- 
sistance, but not to the amount of work produced and 
transformed into heat in the resistance. Inserting the 
value for E from equation 1, we find the average electro- 
motive force 

E1 = 2z lo 2 

z being, as before, the total number of lines contained in 

71 

the space swept by the wire, whilst — is the number of 

revolutions per second. 

In the ideal alternating current dynamo represented 
m Fig. 13, the wire in which the currents are generated 
is arranged to one side of the spindle only. We could 
easily improve the design by carrying the wire symmetri- 
cally to the other side of the spindle, but insulated from 
it, and attach its end to a second metal sleeve insulated 
from M. The contact spring or brush B 2 would then have 
to be set so as to touch this second sleeve, and since the 
electro-motive forces created in the two wires are at any 
moment in the same direction as regards the circuit — 
although opposite as regards a fixed point in space — this 
improved dynamo with two wires will give double the 
electro-motive force of the original arrangement. We 
could still further increase the electro-motive force by 
coiling the wire several times round the axis, forming a 
rectangular coil, each convolution being insulated from 
its neighbours, and if the number of turns counted on 
both sides of the spindle is Nt, the average electro-motive 
force will be 

For most practical purposes, and especially for the trans- 



IDEAL CONTINUOUS CURRENT DYNAMO. 71 

iiiission of energy, alternating currents are, however, not 
so convenient as continuous currents, and to produce the 
latter it will be necessary to add to our dynamo a device 
by which the currents are all directed to flow in the same 
sense as far as the external circuit is concerned. Such a 
device is the commutator, and its action can be explained 
by reference to Fig. 14. In the position shown, the 
electro-motive force created in the wire a b will be 
directed towards the observer, and that created in the 
wire c d will be directed from the observer. The ends 

Fig. 14. 



IDEAL CONTINUOUS CURRENT DYNAMO. 

of these wires are joined at the back by a cross connec- 
tion a c, and at the front by two wires df and b g, to 
the two halves of a metal cylinder, which for the purpose 
of insulation are secured on a wooden hub. The electro- 
motive forces created in d c and a b tend to draw a cur- 
rent from the line in the direction of the arrow to the 
brush B l3 thence through f d, c a, b g, to the brush i? 2 , 
and out again into the external circuit. This process will 
go on until the crank reaches the lower vertical position, 
the strength of the current meanwhile decreasing to zero. 
When the crank is vertical, each brush touches simul- 
taneously both halves of the metal cylinder or com- 



72 



ELECTRIC TRANSMISSION OF ENERGY. 



mutator, as it is technically termed, and a moment later 
the connections become reversed, the brush B 2 now 
touching the half cylinder to which the wire f is at- 
tached, and the brush B L touching the half cylinder to 
which the wire g is attached. But, at the same time, the 
direction of electro-motive force in the two wires has been 
reversed, the wire c d entering the right-hand side of the 
field, and a b entering the left-hand side. Consequently 
the external current flows in the same direction as before, 
growing from zero to a maximum when the crank stands 
horizontally on the left, and again diminishing to zero 
when it is vertical. Graphically represented, the current 



Fig. 15. 



a *~v 



--£ 




2 



is of the character shown by the curve, Fig. 15, the 
abscissas being consecutive angles of the crank, and the 
ordinates being proportional to the sines of these angles. 
It should be noted that the reversal of current always 
takes place when the electro-motive force is zero, and con- 
sequently the change in the contact with the brushes from 
one commutator plate to the other takes place without 
sparking. To increase the power of the machine, we can 
replace the single rectangle of wire by a coil of many 
turns. Fig. 16. Hitherto we have tacitly assumed that 
the space contained within the wire coils forming the 
armature contains air or other non-magnetic substance. 
The lines of force passing between the polar surfaces 
S Nh&ve to leap across a considerable air space, and if 



SHUTTLE-WOUND ARMATURE. 73 

by some means we could shorten that portion of their 
path which lies entirely in air, we would facilitate the 
flow of lines and increase the strength of the magnetic 
field. Roughly speaking, we may take it that air offers 
to the lines of force about 800 times the resistance of 
iron, and if we can contrive to fill part of the space 
between the polar surfaces with iron, a considerable in- 
crease of electro-motive force, and consequently of cur- 
rent, will be the result. The space available for this 
purpose is that contained within the armature coil ; in 
other words, to increase the power of the machine we 
must wind the armature coils over an iron core. An early 

Fig. 16. 




dynamo constructed on this principle is that of Siemens, 
invented in 1855, and provided with the so-called shuttle- 
wound armature. The core consists of an iron cylinder 
provided with two deep longitudinal grooves placed oppo- 
site so that the cross-section resembles a double T with 
rounded heads. The wire is wound into these grooves, 
and the two ends of it are joined to the plates of a two- 
part commutator. Fig. 17 shows a cross-section of this 
armature. In the first machines the core was in one 
solid piece, but it was found to heat considerably on 
account of internal currents. It is well known that if a 
solid body of metal be rapidly rotated between two 
powerful magnet poles it becomes hot. The reason for 
this phenomenon is that the outer portions of the metal 



74 



ELECTRIC TRANSMISSION OF ENERGY. 



in cutting through the lines of force become themselves 
the seat of electro-motive forces acting at right angles to 
the direction of motion and to the lines, and powerful 
currents are started parallel to the axis which run in 
opposite directions, up on one side and down on the other 
side of the axis. In a solid armature core there is 
nothing to check the flow of these currents but the re- 
sistance of the metal, which, on account of the large 
cross-sectional area, is extremely low. These wasteful 
currents are consequently very strong, and not only 
absorb much power, but they also weaken the current 
generated in the copper wire by induction. To avoid 

Fig. 17. 




SIEMENS SHUTTLE- WOUND ARMATURE. 

their creation, it is necessary to subdivide the mass of the 
core by planes at right angles to the axis, and to insulate 
as much as possible the subdivided portions from each 
other. This can be done either by cutting deep narrow 
circular grooves in the core, or by building it up of thin 
discs insulated from each other either by paper discs or 
by being coated with some insulating paint. These arma- 
tures are not much used for dynamos at the present day, 
having been replaced by more perfect forms to be de- 
scribed presently ; but they are still extensively employed 
for small electro-motors. By referring to Fig. 15 it will 
be seen that the counter-electro-motive force of these 
motors is a variable quantity depending on the angular 
position of the armature. If the heads of the double 



SHUTTLE-WOUND ARMATURE, 75 

T core are opposite the field magnet poles, the coil is at 
right angles to the lines of force and the counter-electro- 
motive force is zero. This happens precisely at the moment 
when the brushes touch simultaneously both plates of 
the commutator, and are therefore short circuited. A 
current sent through the motor while at rest in this 
position cannot start it, and this condition is expressed by 
saying that the armature has two dead points. When at 
work the momentum of the armature is sufficient to carry 
it over the dead points, and, apart from the inconvenience 
to have to start the motor occasionally by hand, these 
dead points present no mechanical imperfection. But it 
might be thought that they present a serious electrical 
imperfection for the following reason : The strength of 
the current which is allowed to pass through the motor 
at any given moment depends partly on the electrical 
resistance of the motor, and partly on its counter-electro- 
motive force at that particular moment. But since at the 
dead points there is no counter- electro-motive force, the 
strength of the current will be a maximum, whilst at 
those moments the mechanical energy produced is nil. 
We assume here that the motor is fed by a current flowing 
under a constant electro-motive force, which is the case 
most commonly met with in practice. We have now to 
distinguish between two cases : the motor may be either 
series wound or shunt wound. If the former, the current 
is passing through the motor whilst the armature is at a 
dead point has only to overcome the resistance of the 
field magnet coils. If the armature is in the position of 
greatest counter-electro-motive force the current has to 
overcome not only that, but also the combined resistance 
of field magnet and armature coils. In that position the 
mechanical energy of the armature is at its greatest 



76 ELECTRIC TRANSMISSION OF ENERGY. 

value, but the strength of the current is a minimum. We 
find; therefore, on the one hand, that the strength of the 
field magnets (which depends on the current) is least at 
the very moments when the armature is in a position 
to exert most power, and on the other hand, that it is 
greatest when the armature is at its dead points and can- 
not exert any power. From the foregoing w r e should 
expect that twice during each revolution a great waste 
of current must take place when momentarily the brushes 
are short-circuited by the commutator. Although the time 
during which such short circuits lasts may appear to our 
senses very brief, it would in comparison with the speed 
of electric phenomena be still considerable, and have an 
appreciable effect on the economy of the motor. But 
there is one circumstance which greatly tends to mitigate 
the evil effect of the dead points just described, and this 
is the property of electric currents called self-induction. 
It can best be described as a kind of inertia opposing 
any sudden change in the strength of the current. If a 
circuit contains a coil of wire surrounding iron (as in the 
present case the field magnets) the self-induction is so 
great that it requires an appreciable time to change the 
strength of the current. The increase of current at the 
dead points is, therefore, checked by this property of self- 
induction, and the current, instead of being subjected to 
abrupt and violent changes, becomes simply undulatory. 
The case is different if the motor be shunt-wound and 
fed from a source of constant electro-motive force. Since 
the field magnet coils are excited independently from the 
current which passes through the armature, their self- 
induction cannot in any way steady that current, and 
abrupt changes in its strength and great waste of 
electrical energy must occur at the dead points. This is 



EXPERIMENTS ON SELF-INDUCTION 77 

a matter of considerable practical importance, and shows 
that motors with shuttle-wound armatures should never 
be used coupled up otherwise than armature and field 
magnets in series. If it be absolutely necessary to use a 
motor of that class, the field magnets of which are either 
permanent steel magnets or are electro-magnets excited 
independently, the waste can to a certain extent be pre- 
vented by inserting into the armature circuit an electro- 
magnet which will by its self-induction steady the current. 
Since this point is of importance, the author has thought 
it necessary to verify the above theory by experiments. 
These were undertaken with a twofold object. First, to 
prove that in a series-wound motor there is no appreciable 
waste of current at the dead points, and, secondly, to 
prove that in a motor the field magnets of which are 
separately excited, such waste occurs. The experiments 
were carried out as follows. Two small Griscom motors 
were placed in line behind each other, and their spindles 
were coupled, so that the armatures stood at right angles 
to each other, that is to say, when one armature was at its 
dead point the other was in the position of best action, 
and its counter-electro-motive force was a maximum. 
This disposition is represented in Fig. 15 by the dotted 
curve overlapping that shown in full lines by 90°. The 
resultant counter-electro-motive force is at any point the 
sum of the ordinates of the two curves, and is shown by 
the undulating line a b. It will be seen that this curve 
nowhere touches the horizontal and, therefore, the total 
counter-electro-motive force of the two motors coupled in 
series never is zero. An abnormal rush of current at the 
dead points of any of the armatures can, therefore, not 
take place. The motors were supplied with a current, 
the electro-motive force of which was kept as nearly as 



78 ELECTRIC TRANSMISSION OF ENERGY. 

possible constant during each experiment, whilst the 
mechanical energy developed was measured on one of the 
author's absorption dynamometers. The commercial effi- 
ciency of the two motors combined was thus ascertained, 
as shown in Table I. The motors were then coupled 
parallel, and their efficiency was determined under the 
same conditions. In this case there were, during each 
revolution, four dead points, at which the counter- 
electro-motive force was zero, and when an abnormal 
rush of current could take place if not checked by the 
self-induction of the magnet coils. As was to be ex- 
pected, the current passing through both motors was about 
double, and its electro-motive force was about half of 
the former values. But the commercial efficiency w r as 
about the same, Table II. One motor alone was then 
tried, and its commercial efficiency was found to be about 
the same as that of the two motors combined, Table 
III. The field magnets of both motors were then excited 
separately, and the armatures coupled at right angles 
and connected in series, as per Fig. 15, when the com- 
mercial efficiency was found to be rather higher than in 
the former experiments, Table IV. This is but natural, 
because the energy necessary to excite the field magnets 
w r as not taken into account when calculating the efficiency. 
The two armatures were then coupled parallel — field 
magnets still independently excited — and thus during 
each revolution there were four points where the counter- 
electro-motive force was zero and waste of current did 
take place, as is clearly shown by the low efficiency in 
Table V. One motor alone was then tried under the same 
conditions and the same result was found, Table VI. 
These experiments prove conclusively that our above 
reasoning about the effects of the dead points is correct. 



EXPERIMENTS OF SELF-INDUCTION, 



79 



Test of Tv:o Griscom Motors, Numbers 1017 and 1027. 



Resistance of . 


. N° 1017 . 


. N° 1027 


Armature 


•328 . 


•352 


Magnets 


•596 . 


•522 


Total . . 


•924 . 


•874 



Table I. Armatures Coupled at Right Angles, both Field 
Magnets and Armatures connected in Series. 



Revolutions per 
minute. 


Current. 


E. M. F. 


Foot Pounds 
on Brake. 


Commercial 
Efficiency %. 


2,440 
2,368 
2,440 


1-31 

3-85 
3-50 


6-90 
18-20 
16-00 



588 
535 



19-0 
21'7 



Table II. Armatures Coupled at Right Angles. Each 
Armature in Series with its Field. Both Motors connected 
Parallel. 



Revolutions per 
minute. 



2,120 

2,480 
2,775 
2,340 
2,060 
2,884 
2,328 



Current. 


E. M. F. 


2-35 


2-94 


5-25 


6-05 


6-60 


7-57 


6-80 


7-52 


7-50 


7-63 


7-90 


9-27 


7-60 


8-50 



Foot Pounds 
on Brake. 





206 
432 
366 
450 

748 
578 



Commercial 
Efficiency %. 




14-7 
19-5 
16-3 
18-0 
23-0 
210 



80 



ELECTRIC TRANSMISSION OF ENERGY. 



Table III. One Motor only. Armature and Field Mag- 
nets connected in Series. 



Revolutions per 
minute. 



1,980 
2,024 
1,772 
2,334 
1,954 
2,241 
2,118 
2,070 



Current. 


E. M. F. 


1-02 


4-00 


4-15 


8-20 


4-15 


8-40 


4-22 


9-25 


3-82 


8-10 


3-70 


8-25 


3-50 


7-60 


5-37 


12-00 



Foot Pounds 
on Brake. 



o 

303 

265 
381 
246 
283 
240 
532 



Commercial 
Efficiency %. 




28-0 
17-0 
22-3 
18-0 
20-9 
20-5 
18-6 



Table IV. Armatures coupled at Right Angles and Con- 
nected in Series. Field Magnets excited separately. 



Revolutions per 
minute. 


Current. 


E. M. F. 


Foot Pounds 
on Brake. 


Commercial 
Efficiency °/ . 


1,536 
2,030 
1,632 
2,190 
2,264 


1-42 
3-30 
3-10 
3-70 
3-93 


7-20 
11-10 

9-50 
12-90 
13-40 




370 
300 
483 
500 




22-8 
23-2 
22-7 
21-4 



Table V. Armatures Coupled at Right Angles and Con- 
nected in Parallel. Field Magnets excited separately. 



Revolutions per 
minute. 

2,000 
3,040 
1,094 
1,746 
1,680 



Current. 


E. M. F. 


3-90 


4-40 


4-50 


5-20 


7-50 


5-50 


8-50 


6-60 


9-10 


7-50 



Foot Pounds 
on Brake. 






242 
385 
396 



Commercial 
Efficiency %. 



o 
o 

13-3 
15-6 
13-1 



I 



HEFNER-ALTENECK ARMATURE. 



81 



Table VI. One Motor only. Field Magnets excited 

separately. 



Revolutions per 
minute. 


Current. 


E. M. F. 


Foot Pounds 
on Brake. 


Commercial 
Efficiency %• 


1,778 
2,330 
2,422 


1-65 
4-80 
4-75 


3-80 
5-60 
5-80 



87 
126 




7-4 
10-3 



As already mentioned, motors with ordinary shuttle- 
wound armatures have the disadvantage of requiring to 
be started by hand if they happen to have stopped on a 
dead point. They are, consequently, only made of 
small size, and for larger motors armatures without dead 
points are used. Such an armature can be evolved out 
of the simple shuttle-wound pattern by employing two 
sets of coils placed at right angles to each other. This 
arrangement is shown in Fig. 18, which represents the 
Hefner- Alteneck winding invented in 1872. In order to 
avoid complication the shaft is omitted and the core is 
indicated by two dotted circles. From what has already 
been explained it will be seen that in all those wires 
which at a given moment lie on the right hand side of the 
vertical centre line, the electro-motive force is directed 
towards the observer, and in all the wires lying to 
the left of that line it is directed from the observer. 
The diameter of commutation joining the points of con- 
tact of the brushes with the commutator cylinder will, 
therefore, be horizontal. In the position shown the nega- 
tive, or left brush, will touch segment Z>, and the right 
or positive brush will touch segment B. The current 
enters the armature at the negative brush and splits into 
two circuits as follows : — One portion goes through VII., 

G 



82 



ELECTRIC TRANSMISSION OF ENERGY. 



7, 8, VIII., I., 1, 2, II., and out by the positive segment 
B ; the other goes through VL, 6, 5, V., IV., 4, 3, III., 

and out by the same segment B. The two currents are, 
therefore, in parallel connection. When the armature 
has turned so far as to bring the segment C into contact 
with the negative brush it will touch for a short time 
both segments D and C, whilst the positive brush will 

Fig. 18. 




HEFNER-ALTENECK ARMATURE. 



simultaneously touch A and B. In this position the 
wires I., VI., V., II. will be in the strongest part of the 
field, and the wires VII., IV., III., VIII. will stand on 
the vertical diameter and contribute nothing towards the 
total electro-motive force. The current now splits into the 
following two circuits : From D to VI., 6, 5, V., to A, 
and from C to I., 1, 2, II., to B. In this case the total 



HEFNER-ALTENECK ARMATURE. 83 

electro-motive force is that due to two wires in the position 
of best action, whereas in all the other positions it is due 
to four wires. It has been shown above that the average 
electro-motive force of a loop such as I., 1, 2, IL, con- 
sisting of two external wires (Nt = 2) is 

^ = 2,^2. 

Since two such loops are placed in series, we find the 
average electro-motive force of the whole armature 

But 8 is the number of wires counted all round the 
armature ; and if, instead of a four-part commutator, we 
had employed a six-part commutator, and had wound the 
core with three sets of double coils, we would have three 
coils in series and the expression for Ea would have been 

Ea=l2Z^, 

there being twelve external wires on the armature if 
counted all around. We might thus construct armatures 
with any even number of external wires. Let Nt be that 
number, and we have the general expression for the 
electro-motive force created in the armature of a dynamo, 
or the counter-electro-motive force created in the armature 
of a motor : 

Ea = NtZ ~ 6 

For the sake of simplicity we have, in Fig. 18, only shown 
one wire to each coil. It is, however, obvious that by 
multiplying the turns or wires in each coil the electro- 
motive force can be proportionately increased. This case 
is provided for in formula 3, where iVsignifies the number 



84 



ELECTRIC TRANSMISSION OF ENERGY. 



of coils, and t the number of turns in each coil, the pro- 
duct of the two being equal to the total number of single 
wires if counted all around the armature. An armature 
of the Hefner-Alteneck pattern with eight-part commu- 
tator, is shown in Fig. 19. Denoting by Roman figures 
the ends of the wires on the front end of the armature, 

Fiff. 19. 




3 H 

HEFNER-ALTENECK ARMATURE. 



From the 
negative 
brush to 



and by Arab figures those on the rear end, the winding is 
as follows : 

I., 1, 2, II., III., 3, 4, IV., V., 5, 6/ 

VI., VII., 7, 8, VIII. To the 

XVI., 16, 15, XV., XIV., 14, 13, [positive 
XIII., XII., 12, 11, XI., X., 10, brush 
9, IX. 

The greater the number of parts in the commutator the 
more nearly constant will be the electro-motive force and 
current. This system of winding armatures has the great 
advantage of utilizing nearly the whole length of the 
wire, since, with the exception of the cross connections at 
the ends, all the wire is active. But it has the practical 
disadvantage that repairs are troublesome to execute. If 
a fault of insulation should develop in any of the coils, 



GRAMME ARMATURE. 



85 



in order to reach it, a large portion of the wire must be 
taken off, because the coils — especially at the ends — 
overlap each other in many layers. In this respect the 
style of armature known as the Gramme, or Pacinotti 
type, is preferable. A circular iron ring, Fig. 20, is 

Fig. 20. 




GRAMME ARMATURE. 



wound with a continuous helix of insulated copper wire, 
and certain points of the helix are joined by connecting 
wires, which in our illustration are shown radial, to the 
commutator plates. Two brushes, B x and 2? 2 , serve as 
connections between the external circuit and the armature 
wire. The action of the Gramme armature will best be 
explained by reference to Fig. 21, which shows the lines 
of force. It has already been pointed out that iron offers 
very much less resistance to the passage of magnetic lines 
of force than air. If there be no armature between the 
field magnet poles, we assume that the majority of the 
lines will go straight from pole to pole, Fig. 22. If now 
a circular core is inserted, their course will be so altered 
that each line takes the path of least resistance — that is, 
runs as long as possible in iron, and only leaps across the 



86 



ELECTRIC TRANSMISSION OF ENERGY. 



air at the external circumference of the core, because this 
is the only way in which it can enter the pole piece, 
Fig. 23. At the internal circumference of the armature 



Fiff. 21, 




there is no necessity for the lines to leave the core, and 
the central space is therefore almost free of lines. We say 
almost, because parallel lines exert a repelling action upon 

Fig. 22. 
















■ 










MA 



' ' '< < ; - 

^-^.^-^•.>X;:>/-..<.--.v:-V.-.!r.-..^-.A.-\ 



FIELD OF DYNAMO WITH ARMATURE REMOVED. 

each other, and it may happen that in case the core is thin, 
and a large number of lines have to be accommodated, 
some of them may be elbowed out into the central space. 



FIELD OF DYNAMO. 



87 



In well-designed machines the number of lines thus forced 
across the central space is always so small as to be 
omissible. The fact of the central space being free 
from lines ; or, as we may also put it, being shielded by 
the iron of the core from the influence of the magnet 
poles is of great importance, since in consequence of it 
the inner wires of the helix are removed from all induc- 
tive action. If this were not the case electro-motive 

Fig. 23. 




FIELD OF DYNAMO WITH ARMATURE INSERTED. 



forces would be created in these wires, which, being 
opposed to the electro-motive forces developed in the 
external wires, would weaken the power of the machine. 
After what has been explained at length with reference to 
the ideal continuous current dynamo, Fig. 14, it will be 
easy to trace the direction of electro-motive forces in the 
external wires of the Gramme armature, Fig. 20. If 
rotated clock-wise, the electro-motive force will be directed 
towards the observer in all the wires lying to the right of 
the vertical centre line, and from the observer in the wires 



88 ELECTRIC TRANSMISSION OF ENERGY. 

on the opposite side. The two currents resulting from 
these forces are indicated by the arrows. In the wires 1 
and 7, which for the time being move parallel to the direc- 
tion of the lines of force, there is no electro-motive force 
generated, whilst in 4 and 10, which move at right angles 
to the lines, the electro-motive force is a maximum. By 
virtue of the continuity of the helix the electro-motive 
forces in the wires 2, 3, 4, 5, 6 are added, and those in 12, 
11, 10, 9, 8 are also added, the two circuits being at all 
times in parallel connection. The current enters the 
armature at the brush B 2 , which is called negative, then 
splits into the two circuits mentioned, and uniting again 
at the brush JB l9 which is called positive, leaves the 
armature, and enters the external circuit. It will be 
seen from the figure that either brush, when touching two 
consecutive plates of the commutator, establishes a 
metallic connection between the beginning and end of the 
corresponding coil, or, in technical language, short circuits 
that coil. If the brushes are in the position shown — the 
neutral diameter on the commutator — the short circuit is 
perfectly harmless, because there is no electro-motive 
force in the coil ; but if we were to shift the brushes into 
an active part of the field either to the right or left of the 
neutral line, each coil, as its extremities pass under the 
brush, would be traversed by an excessive current, 
causing heavy sparking at the brush, and probably the 
ultimate destruction of the armature. The best position 
at which to place the brushes is always found experimen- 
tally ; it does not accurately coincide with the geometrical 
neutral line, but is found to be in dynamos slightly in 
advance of it, and in motors slightly behind it. Opinions 
are divided as to the reason of this phenomenon. At one 
time it was ascribed to a certain sluggishness in the iron 



GRAMME ARMATURE. 89 

of the core in taking up and losing magnetism, but this 
theory has long since been discarded by most practical 
electricians. Some hold that the shifting of the neutral 
line is due to the magnetizing influence of the armature 
current upon the iron core by which the latter is trans- 
formed into a double horseshoe magnet with like poles 
joined, and the magnetic axis of which stands nearly at 
right angles to that of the field magnets. Others again 
maintain that the brushes must be set forward in a 
dynamo and backward in a motor, on account of the in- 
fluence of self-induction in the armature coils. In reality 
both the last-mentioned causes have something to do with 
the position of the brushes, as will be more particularly 
explained in Chapter IV. 

The first electro-motor having an armature wound on 
the principle above explained, was constructed by Pro- 
fessor Pacinotti, of Pisa, and the design was published in 
the journal " II Nuovo Cimento," in 1864. This machine 
is illustrated in Fig. 24, and the core of the armature 
differed only in so far from that employed by Gramme 
seven years later, as it had external projections between 
the wire coils, which considerably increased the magnetic 
attraction between the armature and the pole pieces, thus 
rendering the machine more powerful. Fig. 25 shows 
part of the core and winding. The core of the Gramme 
machine consists of iron wire coiled into a ring of oblong 
cross-section. After being lapped round with tape for 
the purpose of insulation, it is wound transversely with 
cotton-covered copper wire. The winding consists of a 
number of coils which cover the core completely inside 
and out, and the beginning of each coil is joined with the 
end of its neighbour to the same commutator plate. When 
the winding is completed the armature is driven tight 



90 



ELECTRIC TRANSMISSION OF ENERGY. 



over a wooden centre by which it is fastened to the 
spindle. 

By means of the fundamental formulas established in 
the previous chapter, we can now determine the electro- 
Fig. 24. 




motive force of a Gramme armature. Let D be its dia- 
meter, b its length, and a the radial depth of the core. 

Fig. 25. 




PAC1NOTTI ARMATURE. 



Let Nt represent the total number of external wires, 
counted all around the circumference, t representing the 
number of wires corresponding to one plate in the com- 
mutator, and N the number of plates. If n denotes the 



PACINOTTI ARMATURE. 91 

speed in revolutions per minute, and z the total number 
of lines emanating from one pole and entering the halt 
circumference of the armature, then the average electro- 
motive force created in each wire is by equation 2, 

E - 2 Z 60- 

Nt 
Since — wires are for the time being connected in 
J* 

series, the average total electro-motive force in the arma- 
ture is 



E - = * Nt m 



It might be objected that this expression, which is based 
on equation 2, will only be correct if the condition under 
which this equation was obtained is fulfilled in the 
dynamo. This condition was that the field should be 
perfectly uniform throughout the -space occupied by the 
armature. In reality this is never the case, and the 
exact distribution is not accurately known. A doubt 
might therefore be entertained whether equation 4 be 
rigorously true in the case where the intensity of the field 
is not uniform, but varies in different parts of the field. 
It will consequently be desirable to deduce the formula 
for the electro-motive force under the supposition that 
the intensity of the field in any point on the circumference 
of the armature, is a function of the angle, a, which the 
radius to that point forms with the neutral line. What 
that function is we cannot say, nor is it necessary that 
we should be able to define it. We only make this 
assumption : that there shall not be any abrupt changes 
in the strength of the field. We assume that the density 
of lines varies gradually from place to place. Assume 
also the number of wires on the armature so large, that 



92 ELECTRIC TRANSMISSION OF ENERGY. 

their angular distance A a is very small, in fact so small 
that the intensity of the field can be considered as con- 
stant within that angular distance. Since the electro- 
motive force created in the wires is proportional to their 
speed, we can determine it for any convenient speed, and 
if it be required for a different speed, we can obtain it by 
multiplying the result first obtained with the ratio of the 
two speeds. In the present instance we fix as a conve- 
nient speed that which will bring each wire at the end of 
one second into the position occupied by its immediate^ 
neighbour at the beginning of the second, or 

A D 

This is a very slow speed, and if we wish to know what 
will be the electro-motive force at the faster speed of n 
revolutions a minute, we shall have to multiply the 
electro-motive force at the low speed with the ratio of 

— . 7T . D and v. Since A a Nt = 2 tt we have also 
60 

v = -=r=r- and the ratio of the two speeds is 

J.V6 



71 n 
60 '^ 


— Nt n 


irD 


~ m m 



Nt 
Let F l9 F 2 . . F^ be the intensity of the field at the 

first, second, . . . — - wire, counted from the neutral line, 
on one-half of the circumference of the armature, then 



ELECTRO-MOTIVE FORCE IN ARMATURE. 93 

the electro-motive force in these wires will be given by 
the expressions, 

E x = F x bv 

E 2 = F 2 bv 



ENt = F Ntb v. 

2 ~2~ 

The sum of all these forces gives the total electro-motive 
force created within the armature, which we denote in 
future by E a. 

Ea = ZFbv. 

But the expression F x bv represents the number of lines 
contained between the first and second wire on the arma- 
ture, since F x is the density, and b v the area of the space 
swept by the first wire in one second. Similarly F 2 b v 
represents the number of lines between the second and 
third wire, and so on, the sum of all these expressions re- 
presenting the total number of lines entering between the 
first and last wire on one-half circumference of the arma- 
ture. Let z be that total number, and we find for the 
electro-motive force at the low speed, 

Ea = Z, 

At the high speed we have, therefore, 

**'*'£> 4) 

precisely the same expression as already obtained above. 
If z be inserted in absolute measure, Ea will also be 
obtained in absolute measure, and to obtain it in volts the 
right side of the equation must be multiplied with 10 -\ 
We can also write 



94 ELECTRIC TRANSMISSION OF ENERGY. 

and if we measure the field intensity by means of a unit 
6,000 times as great as the absolute unit, we can further 
simplify the equation to 

E a = Z Ntn 10" 6 , 5) 

Z being the total number of lines in the new system, 
which is related to the absolute system by the equation 

Z = 



6000 

The cross-sectional area of the armature core is 2 a b, and 
if we denote by m the average density of lines per square 
inch of armature core, we have, 

Z = 2 a b m, 
and inserting this value in 5), we find for the electro- 
motive force also the expression, 

JE a = 2abmNtn 10' 6 6). 

This expression is sometimes more convenient than the 
former, because it enables us at once to see how the 
dimensions of the armature affect the electro-motive force. 
Experience has shown that the density of lines, m> in the 
core cannot exceed a certain limit, which is reached when 
the core is saturated with magnetism. This limit is 
m = 30, but in practical work a lower density is gene- 
rally adopted, for reasons which will be explained in the 
following chapter. A fair average value in good modern 
dynamos and motors is m = 20, and the area, a b, must 
be taken as that actually filled by iron, and not the gross 
area of the core. To avoid waste of power and heating, 
the armature core of dynamos and motors must be sub- 
divided into portions insulated from each other, the planes 
of division being parallel to the direction of the lines of 
force, and to the direction of motion. The space wasted by 
such insulation must be deducted from the gross area of 



ELECTRO-MOTIVE FORCE IN ARMATURE. 95 

the core, and the remainder — from 70 to 90 per cent, of 
it — is the portion actually carrying lines of force. 

The electrical energy developed in the armature, if a 
current c be flowing through its coils, is E a c, and the 
horse-power represented by this energy is 

H-P =^-- c2 abmNtn 10*. 

The power to be applied must naturally be somewhat in 
excess of this in order to overcome mechanical resistances, 
as friction in the bearings and air resistance, and also the 
magnetic resistance due to imperfect subdivision and 
heating of the core, and reaction of the armature on the 
magnets. In good dynamos these losses do not exceed 
about 10 per cent, and may even be less. 



CHAPTEE III. 

Reversibility of Dynamo Machines — Different conditions in Dynamos and 
Motors — Theory of Motors — Horsepower of Motors — Losses due to Me- 
chanical and Magnetic Friction — Efficiency of Conversion— Electrical 
Efficiency — Formulas for Dynamos and Motors. 

After what has been explained in the previous chapters 
it will be evident that dynamo machine and electro-motor 
are convertible terms. Any dynamo can be used prac- 
tically as a motor, and in most cases any motor can be 
used to generate a current. On purely theoretical grounds 
this should be possible in all cases, but in practice it is 
found that the speed which is required to make some 
small motors act as self-exciting dynamos is so high as to 
render that application mechanically impossible. The 
reason for this is, that in small motors the polar surfaces 
are of very limited extent, and consequently the magnetic 
resistance of the path traversed by the lines of force is 
excessively high, requiring more electrical energy to 
excite the field magnets than the armature is capable of 
developing at a moderate and practical speed. This point 
will be more fully explained further on. For our present 
purpose it suffices to note that on purely theoretical 
grounds the same machine can act as a motor or as a 
dynamo. A separate investigation as to the theory of 
motors might, therefore, almost seem superfluous. But, 
on the other hand, experience has shown that although 



THEORY OF MOTORS. 97 

this reversibility of the dynamo machine exists, it is not 
always the best dynamo which makes the best motor, and 
that certain details have to be altered according to the 
use for which the machine is intended, if we wish to pro- 
duce the best possible machine for each purpose. The 
conditions which have to be fulfilled in the case of 
dynamos are also generally different from those required 
in motors. The dynamo must have a high efficiency, it 
must be able to work continuously without undue heat- 
ing in any of its parts, must not be injured by an occa- 
sional excess of current, and must work equally well at 
extreme variations of electrical output. Its weight is, as 
a rule, of secondary importance, and in many cases there 
is no objection to large weights. The motors, on the 
other hand, are generally required to be of the smallest 
possible weight, they work intermittently, and high effi- 
ciency, although desirable, is not of so muoh importance, 
especially not in small motors. In the early days of 
electric transmission of energy the difference between the 
conditions in dynamos and motors was overlooked, and 
the usual arrangement was to employ two identical 
machines, one acting as generator, the other as receiver, 
but at the present time this rough-and-ready method does 
not satisfy all the requirements which can justly be made, 
and special motors must be provided. It has thus be- 
come necessary to study the theory of motors apart from 
that of dynamos. 

Let in Fig. 26, N S be the pole pieces and D the mean 
diameter of the annular space filled by the external wires 
on a cylindrical armature of the Gramme or Hefner- 
Alteneck pattern. Let, as before, b represent the length 
of the wire and F the intensity of the field at a given 
point i?, the radius to which forms with the neutral line 

H 



98 



ELECTRIC TRANSMISSION OF ENERGY. 



the angle a. All the wires on the upper half of the arma- 
ture will be traversed by currents flowing in the same 
direction, say from the observer, and all the wires on the 
lower half will be traversed by currents flowing towards 
the observer. Let c be the current in each single wire 
and let there be Nt external wires counted all around the 
circumference. If these wires lie close together with 
only as much space between them as is necessary for 



Fig. 26. 




mutual insulation, the effect of the current c traversing 
successively the — wires on one half of the circumference 

will evidently be the same as that of a semicircular sheet 

Nt 
of current of total strength — c, the width of this sheet 

D 



7T 



measured transversely to the direction of flow being 

The density of current in the sheet, that is, the strength 

e -4. * mo. ' Nt * D Nt c > 
oi current per unit ot width, is — c : — r— = — 

and the current flowing down an elementary section at 



THEORY OF MOTORS. 99 

R, the angular width of which (A oi) we take to be very 
small, is, 

Ntc D A 

The mechanical force tending to rotate the elementary 
strip of our sheet of current in the direction of the arrow 
is 

A P = Fb A c 

at, 77 ,D . Nt c 

AF = Fb 2 A " 7 TJD- 
Now F 9 the intensity of the field, multiplied with 

b - A a 9 the total area of the elementary strip, gives 

the number of lines of force which enter the core through 
that area. Let A Z represent that number, and we can 
also write 

7T 1) 

Now consider a second elementary strip of the sheet of 
current contiguous to the first. The force exerted by 
this strip will be represented by a similar expression, 
but in it the value of A Z may be different. This will 
be the case if the field intensity is not uniform, but varies 
in any way with the angle a. For our purpose it is not 
necessary to know in what manner the intensity of field 
F may vary in different points ; whatever the law of 
variation may be, the sum of all the values of A Z must 
always be the same, and equal to the total number of 
lines passing into the armature core. The mechanical 
force exerted by the upper semicircular sheet of current, 
or, which comes to the same thing, by the upper half of 

the armature winding, -- , is therefore 

J* 



100 ELECTRIC TRANSMISSION OF ENERGY. 

Ntc 

Z being the total number of lines. Simultaneously the 
lower half of the armature exerts the same force, and we 
have the total force tending to rotate the armature, and 

acting at a radius equal to that of the winding, — , 

2Z Ntc 



P = 



it 



D 



The turning moment, or torque, is P — , or 

r -**-'. 7). 

7T 

If we express the total number of lines by the product of 
their density within the armature core and the dimensions 
of the latter, we can also write for the torque 

T = 2 ah m Ntc 

It has already been mentioned that there exists a limit 
beyond which m cannot be increased, however powerful 
the field magnets may be. Assume that in two motors 
of different size the field magnets are excited so as to 
produce equal and maximum density of lines in both 
armature cores, and assume also that both armatures are 
wound with wire of the same gauge, then the number of 
turns will in the larger machine be greater than in the 
smaller, the proportion being evidently as the squares of 
their linear dimensions. Since the areas of the cores are 
also in the same proportion, it follows that the torques or 
turning moments are in the proportion of the fourth 
power of the linear dimensions. Thus, if the larger 
motor be double the linear dimensions of the smaller, its 



TORQUE EXERTED BY ARMATURE. 101 

torque will be sixteen times as great. It will be seen 
from formula 7, that the torque of a motor depends only 
on the strength of the field and on the current, but does 
not depend on the speed. This can be shown experimen- 
tally in the following manner. Let two series-wound 
dynamos be connected by a pair of cables, and let one of 
these act as generator, whilst the other, which is the 
motor, is provided with a friction brake, on which the 
energy given out can be measured. Whatever the speed 
of the motor may be, the brake, if its lever be floating 
free, indicates the turning moment in the shaft of the 
motor. This turning moment is equal to the product of 
the length of the lever and the load suspended. If now 
the speed of the generator be varied so as to vary the 
electro-motive force, the speed of the motor will accord- 
ingly vary, but the current and the load on the brake 
will remain unaltered. In dealing with this matter, 
M. Marcel Deprez, in " La Lumiere Electrique " of the 
3rd of October, 1885, says: — "If a current traverses a 
motor having an armature of the Pacinotti type, the 
turning effort of the latter is independent of its state of 
movement or rest, and in motion it is independent of the 
speed, provided the strength of the current is maintained 
constant. Inversely, if the static moment tending to 
resist the motion of the armature is maintained constant, 
the current will thereby automatically be kept constant, 
whatever means we may employ to vary it. The experi- 
ment must be made in the following way. Mount upon 
the spindle of the motor a self-adjusting dynamometric 
brake, the load on which is automatically kept constant 
whatever variation may take place in the friction of the 
brake or in the speed of the motor, so that the tangential 
resistance which tends to oppose rotation shall be kept 



102 ELECTRIC TRANSMISSION OF ENERGY. 

constant. Supply the motor with current from any given 
source of electricity (a battery or a dynamo machine), 
and note the strength of the current and its electro- 
motive force. If the latter be gradually increased from 
zero we observe that as long as the motor remains at 
rest the current grows in the same proportion, but as 
soon as it has reached a certain value and the motor 
has begun to turn, the current does not further increase, 
although the rise in the electro-motive force may con- 
tinue, and with it the rise in the speed of the motor. In 
an experiment made three years ago the source of elec- 
tricity was a Gramme dynamo and the motor a Hefner- 
Alteneck machine, the brake being loaded with 5J lbs. 
at a radius of 6f- inches. When the motor began to turn, 
the needle of the ampere-meter indicated twenty-six 
divisions. I then augmented the speed of the dynamo 
until the motor made thirty-two revolutions per second, 
and yet the ampere-meter only indicated twenty-seven 
divisions instead of twenty-six." 

Since with a constant load on the brake, the energy 
given out is proportional to the speed, and since the 
electrical energy supplied to the motor is the product of 
current and electro-motive force, it follows that if the 
current is constant the speed must be proportional to the 
electro-motive force. The following table taken from M. 
Marcel Deprez's article shows that this is indeed the 
case. It will be seen that in all the four motors tested 
the ratio of electro-motive force to speed remained nearly 
constant throughout a very wide range of speed, and that 
the current also remained practically constant 



TORQUE INDEPENDENT OF SPEED. 



103 



Type of motor. 


Revolutions 
per minute. 


Current. 


Electro-motive 
force. 


Speed. 


Hefner-Alteneck . -J 


425 

783 

1165 

1660 


13-53 
12*68 
13-65 
13-00 


•0267 
•0262 
•0278 
•0250 


A Gramme . • . < 

V 


270 

526 

608 

742 

944 

1004 

1160 

1460 


8-16 
8-16 
8-23 
8-40 
8-23 
8-23 
8-23 
8-23 


•06496 
•06437 
•06768 
•06792 
•06713 
•06803 
•06704 
•06736 


Hefner-Alteneck . \ 

\ 


356 
618 
1016 
1236 
1470 
1636 
1662 


5-60 
5-78 
5-42 
5-60 
5-95 
5-60 
5-42 


•0132 
•0139 
•0127 
•0130 
•0129 
•0127 
•0127 


High tension ma- J 
chine .".'•-." 


200 

384 
470 
606 
710 


5-60 
6-30 
6-12 
5-95 
5-95 


1-659 
1-692 
1-775 
1-633 
1-662 



Going now back to equation 7), the mechanical energy 
represented by one revolution of the motor shaft is 
evidently 2 tt T, and if the motor runs at a speed of n 

revolutions a minute, or — revolutions a second, the 



60 



energy developed during that time is 



n 



W = ZNt2c — 



9). 



104 ELECTRIC TRANSMISSION OF ENERGY. 

It will be remembered that each half of the armature 
carries the current c ; 2c is consequently the total cur- 
rent passing into the armature at one brush and out at 
the other. Write Ca (armature current) for 2c and we 
have 

JF= ZNt~Ca 10). 

But from equation 4) we found that the counter electro- 
motive force of the armature is 

Ea = ZNt~ 4), 

and combining the two equations we find 

W= Ea Ca 11). 

The mechanical energy equals the product of current 
and electro-motive force, that is, equals the electrical 
energy. This, indeed, is self-evident from the principle 
of the conservation of energy ; and starting with the 
equations 4) and 11), we could have deduced the expres- 
sions for W and T from these. But on the other hand it 
is more satisfactory to have determined these values inde- 
pendently, and to find that our conclusions are verified 
by the principle of the conservation of energy. 

All the equations above are based on the absolute 
system of measurement. For practical purposes, how- 
ever, the employment of these units is not convenient, 
and instead of using dynes or ergs we prefer to make our 
calculation in pounds and horse-powers. It will therefore 
be necessary to determine the relation between the abso- 
lute and practical units. 

According to the definition of the dyne given in the 
first chapter, it is that force which accelerates the mass 
of one gram by one centimeter in one second. It would 



ENERGY GIVEN OUT. 105 

not be strictly correct to represent the dyne as equal to 
a certain fraction of a kilogram or of a pound, because 
the weight of unit mass (that of one gram) changes 
according to the position on the surface of the earth 
where we may happen to measure it. But in all places 
the following equations hold good : — 

P = m p, 

G = m g. 
P being the force to which corresponds the acceleration 
p, G being the weight of the body measured by the 
acceleration of gravity g, and m being the mass of the 
body 

P=G P -. 

9 
If g be given in meters per second and the weight in 

kilograms, the force of one dyne is, 

10- 3 10~ a 
Dyne = — .... kilograms. 

10" 5 
Dyne = kilograms. 

The energy represented by one dyne acting through the 
distance of one centimeter, the erg, is therefore 

10~ 5 

. . . kilogram-centimeters, or. 

9 

Erg = . . . kilogram-meters. 

According to equation 11) the number of ergs developed 
by the armature of the motor is numerically equal to the 
product of current and electro-motive force in absolute 
measure. If we wish to insert these values expressed in 
practical units of amperes and volts we have 

W= 10 8 x 10 + 1 . . . voltamperes, 
W= lO" 7 watts. 



106 ELECTRIC TRANS3IISSI0N OF ENERGY. 

To obtain the number of watts represented by a certain 
number of ergs, we have therefore to multiply the latter 
by 10~ 7 . Similarly to obtain the number of kilogram- 
meters represented by a certain number of ergs, we have 

io- 7 

to multiply the latter by > 

Watts = 10~ 7 x ergs, 

IO" 7 
Kilogram-meters = x ergs. 

From these two equations we find that 

Watts 

Kilogram-meters = . 

9 
The energy required to lift 75 kilograms one meter high 

in one second is a standard horse-power in the metric 
system. The acceleration of gravity may be taken as 
9*81 meters per second, hence one horse-power is repre- 
sented by 

75 x 9*81 . . . watts, or in round numbers : 
736 watts correspond to one standard horse-power. 
In English measure the standard horse-power is equal to 
32,500 foot pounds work done per minute. The usual 
English horse-power is equal to 33,000 foot pounds. 
Hence, to obtain the number of watts representing an 
English horse-power, we must multiply 736 with the ratio 
of 33,000 to 32,500. This gives the figure 746. Let 
Ea represent the counter-electro-motive force of the arma- 
ture in volts, and Ca the current in amperes, then the 
number of English horse-powers which could be obtained 
from it, if there w r ere no losses, is 

H-P= E ^ 12). 

Retaining the notation of equations 5) and 6), we have 
also 



BORSE-POWER GIVEN OUT, 107 

HP = ^ Z Ntn 10- 6 Ca . . , . . 13), 

H-P = ^- 2abmNtn 10~ 6 Ca . . . 14). 

The power which is actually obtainable is somewhat 
smaller, as certain losses occur. These might be classi- 
fied under two headings, mechanical friction and mag- 
netic friction. The former consists of the friction in the 
journals, of that between the commutator and the brushes, 
and of the resistance which the air offers to the rapid 
rotation of the armature, or the "windage," as it is techni- 
cally termed. The magnetic friction is of a somewhat 
complicated nature, and may manifest itself in various 
ways, but more especially in the heating of the armature 
core and of the pole pieces. If the armature core is not 
sufficiently subdivided, a fault very common in small 
motors, currents will be generated in it, which will be the 
stronger the more intense the field and the quicker the 
speed. It is as though the motor contained within itself 
a dynamo working on short circuit, and the power neces- 
sary for producing these currents must be supplied by the 
current flowing through the coils of the armature, and re- 
presents therefore so much power withdrawn from external 
use. Another source of loss is the limited number of the 
sections in the commutator. In establishing our formulas 
we have assumed that the aggregate of the currents in 
the different wires can be represented by a continuous 
semicircular sheet of current. This assumption is, strictly 
speaking, only correct if the number of wires and the 
corresponding number of sections is infinite. But when 
these numbers are limited, and especially when one sec- 
tion of the commutator corresponds to a wide coil, con- 



108 ELECTRIC TRANSMISSION OF ENERGY. 

sisting of a great many turns of wire on the armature, 
then the change of contact between the brushes and suc- 
cessive commutator strips produces abrupt changes in 
the magnetizing effect of the current on the core of the 
armature, and our sheet of current, instead of being fixed 
in space as first assumed, undergoes violent oscillations, 
the amplitude of which is equal to the angular distance 
between two neighbouring coils. It is as though a 
magnet placed at right angles to the centre line through 
the pole pieces were kept in rapid oscillation, and since 
any magnet, if moved in the neighbourhood of metallic 
masses will heat the latter and absorb power, it follows 
that the pole pieces will become hot, and part of the 
energy produced by the motor will be wasted in this way. 
From what has just been explained, it will be evident 
that this loss can be reduced by increasing the number of 
sections in the commutator, and by subdividing the metal 
of the pole pieces by planes at right angles to the axis of 
the armature. 

Another source of loss in some motors is the discon- 
tinuity of the armature core. This loss does not occur 
in Gramme armatures with smooth cylindrical cores ; but 
in armatures of the Pacinotti type, the projecting teeth, 
in sweeping closely by the polar surfaces, react on the 
latter, and produce eddy currents therein, which in their 
turn exert a retarding force upon the teeth. That this 
is really the case is shown in a striking manner in many 
dynamos having Pacinotti projections, notably in the 
Brush and Weston machines. Everyone who has 
examined these machines after some hours' work, must 
have noticed that the pole pieces, especially where the 
coils and projections leave them, grow hot. At the 
entering side the heating is not so great, because there 



INTERNAL LOSSES. 109 

the magnetizing effect of the armature current is to repel 
and weaken the lines, whereas at the leaving side it is to 
attract and strengthen them. If the machines be used as 
motors an opposite effect is produced, the pole pieces 
becoming hottest at the entering side. Cores with Paci- 
notti projections are very much in favour with the de- 
signers of motors, because it is thought that they increase 
the magnetic attraction which determines the force of the 
motor. On purely theoretical grounds this is so. It 
will be shown presently that the number of lines Z, pass- 
ing from the pole piece to the armature is the greater, 
the smaller the distance they have to leap through air, 
and by allowing the teeth to project so far as to almost 
touch the polar surfaces, the magnetic resistance of the 
air space can be very considerably reduced. But in prac- 
tice such perfection is unattainable on account of the 
heating and waste of power just explained. It is found 
necessary to make the clearance between the outer sur- 
face of the teeth and the inner surface of the pole pieces 
much greater than would suffice for free rotation, and it 
may be doubted whether the Pacinotti core is, after all, 
so great an improvement over the Gramme core as -on 
purely theoretical grounds it seems to be. There is also 
another source of loss occurring even in armature cores 
w T hich are perfectly subdivided and smooth on the outside. 
This is due to a molecular effect in the iron which has 
been termed hysteresis by Professor Ewing. In ordinary 
motors, having two or four field magnet poles, this loss is, 
however, very small and is generally neglected. 

In good motors the sum total of all the losses here 
enumerated at length amounts to only a small fraction of 
the total power. The ratio between that and the power 
actually obtainable on the shaft is called the efficiency of 



110 ELECTRIC TRANSMISSION OF ENERGY. 

conversion, and it should never be less than 90 per cent, 
in medium-sized and large motors. 

The electrical efficiency of the motor is the ratio of 
total internal electrical horse-power, as given by our for- 
mulas 13) and 14), to the external electrical horse-power 
applied at the terminals of the motor. Let 

E a represent the electro-motive force created in the 
armature coils. 

E h represent the electro-motive force appearing at the 
brushes. 

E t represent the electro-motive force appearing at the 
terminals. 

r a represent the total resistance of the armature. 

r m represent the total resistance of main coils on field 
magnets. 

r s represent the total resistance of shunt coils on field 
magnets. 

(7, C a , C s , C m represent the external current, the current 
through the armature, through the shunt coils and main 
coils on field magnets respectively. Then for a compound- 
wound dynamo, in which the shunt coils are coupled 
across the brushes, the following equations evidently 
obtain : 

E b 

k = f-'m) ^s == — 

r s 

C a = C m + C s 15), 

E h = E a - r a C a 16), 

E t = Ejj — " r m is m .••..«.,. 17 )• 

The electrical efficiency is 

n = £Tc 18) * 



FORMULAS FOR DYNAMOS AND MOTORS. Ill 

For an electro-motor, also compound-wound, the equa- 
tions are 

L a = C m — C s 19), 

E t = E,-r m C m 20), 

E a = E„-r a C a 21), 

«=ff ^ 

If the shunt coils are coupled to the terminals the for- 
mulas are for the dynamo, 

16), 17), and 18) remaining unaltered. 
For the motor we have 



r, 



wJ 



20), 21), and 22) remaining unaltered. 

The same formulas are applicable to the case of plain 
series or shunt machines, whether dynamos or motors, 
but in the case of series machines we insert r s = oo . 
and in the case of shunt machines we insert r m = o. 



CHAPTER IV. 

Types of Field Magnets — Types of Armatures — Exciting Power — Magnetic 
Circuit — Magnetic Kesistance — Formulas for strength of Field — Single 
and Double Magnets — Difficulty in Small Dynamos — Characteristic 
Curves — Pre -Determination of Characteristics — Armature Reaction — 
Horse-power Curves — Speed Characteristics — Application to Electric 
Tramcars. 

In the preceding chapter it has been shown how the 
electro-motive force of an armature can be found if the 
total number of lines passing through its core be known. 
It will now be necessary to determine the number ot 
lines, that is the strength of the magnetic field, from the 
constructive data of the machine. Before entering into a 
scientific investigation of the subject a cursory glance at 
the different types of field magnets adopted by the various 
makers of dynamos and motors, will be of interest. These 
are shown in Figs. 27 to 51. To make the classification 
comprehensive the type of armature is written beneath 
each field and the maker's or designer's name is written 
above it. We distinguish three types of armature. 1. The 
Drum, w r ound on the Hefner- Alteneck principle, as ex- 
plained in Chapter II., and shown in Figs. 18 and 19 ; 
2. The Cylinder, wound on the Pacinotti or Gramme 
principle, also explained in Chapter II., and shown in 
Figs. 25 and 20 ; and 3. The Disc, wound on the Paci- 
notti or Gramme principle and only differing from the 
cylinder by the shape of the core. It is a cylinder of 






TYPES OF FIELDS. 113 

considerable diameter and small length, in fact a flat ring 
or disc. 

All the magnets employed in dynamos or motors are 
horse-shoes ; straight- bar magnets with poles at the ends 
being never used. The reason is obvious. We must in 
all cases bring opposite poles to the same armature, and 
that necessitates the employment of a bent magnet. It 
is necessary to distinguish between single, double, and 
multiple magnets. In the single horse-shoe magnet all 
the lines passing across the armature go through the 
magnet in the same direction. As an example we may 
take the Edison-Hopkinson dynamo, Fig. 27. The lines 
passing across the armature from N to S continue all in 
the same direction, viz., vertically upwards from S to B, 
thence across the yoke from B to A, and finally vertically, 
downwards from A to N. A free unit pole would be 
urged along the closed magnetic circuit N S B A N, and 
there is no other way along which it could travel. Now 
in a double horse-shoe, as represented for instance by the 
Weston machine, Fig. 41, there are two ways along 
which a unit pole might travel. One of these is N SB AN, 
and the other N S D C N, or in other words, of the total 
number of lines passing across the armature, one half will 
go through the horse-shoe NABS, and the other half 
will go through the horse-shoe N C D S. We may con- 
sider the field magnets to consist of these two horse-shoes 
placed with like poles in contact to the left and right of 
the vertical center line. The arrangement of the " Man- 
chester" dynamo is similar, but in this case the portions 
A B and C D 3 which in the Weston dynamo constitute 
the yokes, form the excited or active parts of the magnets 
and are surrounded by the magnetizing coils. The field 
magnets of the original Gramme dynamo (or motor) also 

i 



114 ELECTRIC TRANS31ISSI0N OF ENERGY. 

belong to the double horse-shoe pattern. But in this case 
a plane laid through the center lines of the cores of the 
magnets is parallel to and contains the center line of 
armature shafts whereas in the Weston type it is at 
right angles to it. Here, again, the lines are split up to 
the right and left of the vertical center line into two 
distinct circuits. Fig. 37 shows a similar arrangement, 
but with a single magnet. Figs. 39, 40, and 50 show 
single magnets, the plane of the horse-shoe being at right 
angles to the armature. Fig. 48 shows a quadruple 
horse-shoe magnet. Here the lines of force passing across 
the armature belong to four distinct circuits : S D A N, 
S D C N 9 S B AN, and S B C N. The field magnets 
of the Mordey- Victoria machine shown in Figs. 46 and 47 
consist of 8 complete horse-shoes, four on each side of the 
disc, and in some multipolar machines even a larger num- 
ber of magnetic circuits is sometimes employed. The 
machines which M. Marcel Deprez employed in his ex- 
periments (Fig. 51) had two cylinder armatures mounted 
on the same spindle a b, and around them were placed 
eight horse-shoes, of which two, S B A N and S C D N, 
are shown in the illustration. It is not necessary to enter 
into a detailed description of all the types shown, as the 
diagrams are sufficiently clear. 

After what has been said above it will be evident that 
the proper function of the field magnets in a dynamo or 
motor is to produce lines of force which pass across the 
armature core. All other lines which miss the armature 
are useless and may even be detrimental to the working 
of the machine. The greater the number of useful lines 
the greater will be the electro-motive force generated at 
a given speed and with a given armature. Our aim 
should therefore be to produce a maximum number of 




Fig. 34. 

GOOLDEN AND TROTTER. 



NDE; 




SHORT CYLINDER. 



Fig. 42. 
Maxim. 




CYLINDER. 



Fig. 50. 

JURGENSEN. 




CYLINDER. 




SHORT CYLINDER. 



Fig. 43. 

Thomson-Houston. 




sphere. 



Fig. 51. 
Marcel-Deprez. 






TWO CYLINDERS. 

To face page 114. 



M--.r 



. i_^_ 






r 



'v_o - 





m 



Fig. 39. Fig. 40. 

KAPP. Kapp. 



/:..v--^...::r 



W . ' - 



o ^ 



MAGNETIC RESISTANCE. 115 

lines, and as a first step towards the realization of this 
object we must determine the relation between the number 
of lines and the constructive data of the machine. One 
of these data is the exciting power, that is the product of 
the number of turns of wire wound on the magnet, and 
the magnetizing current sent through the wire. It is 
customary to reckon the exciting power in Ampere- Turns, 
and it is shown by experiment and theory that the manner 
in which the product is made up is quite immaterial. 
We may have a large number of turns of fine wire and a 
small current, or we may have few turns of stout wire 
and a large current. The effect will always be the same 
if the product of amperes and turns be the same. Ex- 
periment also shows that for low degrees of magnetization, 
the electro-motive force produced in the armature is pro- 
portional, or nearly so, to the exciting power X applied 
to the field magnets ; and since electro-motive force and 
strength of field Z are always proportional, we find that 
in these cases Z is proportional to X. We can represent 
this relation mathematically by introducing the concep- 
tion of magnetic resistance. According to this there is in 
every magnetic circuit a passive force opposing the crea- 
tion of lines, and the number of lines which are created is 
the quotient of the magnetizing force and this resistance. 
Calling the latter 22, we have 

Z = f 23). 

This formula is rigorously correct, provided we succeed 
in determining the magnetic resistance for every condition 
of magnetization. For low degrees of magnetization the 
resistance is nearly constant, and in these cases there 
exists simple proportionality between Z and X; for higher 



116 ELECTRIC TRANSMISSION OF ENERGY. 

degrees of magnetization the resistance increases and the 
relation between Z and X becomes more complicated. 
A limit is ultimately approached beyond which we 
cannot increase the strength of the field although w r e may 
increase the exciting power indefinitely. In this case the 
magnetic resistance has become infinite, and this condition 
is generally expressed by saying the magnet is saturated. 
The relations existing between magnetizing power and 
the magnetic moment have in the case of straight-bar 
magnets, spheres, and ellipsoids been investigated by 
Jaeobi, Dub, Miiller, and others, and a variety of 
formulas have been proposed to express these relations 
mathematically. Apart from the fact that these formulas 
in themselves are only rough approximations but imper- 
fectly fitting the results of experiments, they are for 
practical purposes almost useless, since the field magnets 
of dynamos and motors are not straight-bar magnets, but 
horse-shoes of every possible form and variety. In some 
cases these formulas are even misleading, and as an ex- 
ample we may cite the original Edison machines. 
According to the orthodox theory the magnetic moment 
of a cylindrical bar is proportional to some function of 
the exciting power, to the square root of the diameter of 
the bar and to the square root of the cube of its length. 
Hence to obtain a maximum of magnetic moment with a 
given weight of iron we must shape it into a long cylinder, 
and the original Edison machines were constructed on 
these lines. Experience has since then taught us that 
this was the worst possible form which could have been 
adopted, and the Edison machines built subsequently 
have stout and short magnets. The explanation for this 
apparent discrepancy between theory and practice is this, 
that in a dynamo or motor the magnetic moment of each 






MAGNETIC RESISTANCE. 117 

bar composing the field magnet is of no account whatever, 
the electro-motive force depending only on the total 
number of lines produced, which is governed by laws 
totally different from those relating to the magnetic 
moment. It is very desirable that the relations between 
strength of field and exciting power should be mathe- 
matically established for those forms of magnets which 
are actually used in the construction of dynamos and 
motors. As yet no formula rigorously true for all degrees 
of magnetization has been found, and the difficulty is 

Fig. 52. 




principally due to the fact that the chemical composition 
and molecular properties of the, iron play an important 
part which is not easily determinable beforehand. This 
is especially the case if the magnetization is pushed 
tow r ards the saturation limit. For lower degrees of mag- 
netization the difficulties are still present, but they are of 
relatively less importance, and it is possible to establish 
formulas for the strength of the field which are sufficiently 
approximate for practical purposes. 

Let in Fig. 52 a series of wedge-shaped and very short 
magnets, M l M 2 ... be placed with polar faces of oppo- 
site sign in contact, so as to form a continuous ring inter- 



118 ELECTRIC TRANSMISSION OF ENERGY. 

rupted only by the air space, A B, A 1 B 1 . Lines of force 
will then pass across this air space, and an electro-motive 
force could be created by moving a conductor or series of 
conductors, so as to cut these lines. Let the polar sur- 
face of each elementary magnet be S> and let the density 
of magnetic matter, which we imagine to be distributed 
over the polar surfaces, be <r 9 then a S is the strength of 
each polar surface. According to Ampere's theory each 
elementary magnet can be replaced by an equivalent 
magnetic shell (page 28), consisting of a closed con- 
ductor in which a current flows, the product of current 
and area enclosed being numerically equal to the mag- 
netic moment of the elementary magnet. Imagine now 
the magnets replaced by a spiral of wire or solenoid, then 
we can without appreciable error consider each turn of 
wire in the spiral as a current closed in itself, and if 
there be n such turns, and if the current be C, the total 
magnetic moment will be in absolute measure n C S. 
Since with the exception of the two end faces A B, 
A 1 B 1 , the polar surfaces are in contact and cannot exert 
any action at a distance, the total magnetic moment of 
the series of elementary magnets is represented by the 
product of the magnetism on the end farces, and their 
distance, d. We have therefore the equation, 

a S d = n C S. 

It has been shown (page 24), that the total number of 
lines emanating from unit pole is 4 tt. From a pole of 
the strength a- S there must emanate 4 n <t 8 lines. Let 
Z be the total number of lines, or strength of field within 
the air space, then we find 

Z=4:7T<T S, 

and by inserting the value of a S from above equation, 



MAGNETIC RESISTANCE. 119 

_, 47TH CS 



d * 

which can also be written in the form 

nC 



Z = 4 



7T 



d 

s 



The product n C is exciting power in absolute measure, 
or ampere turns x 10 _1 . S is the polar surface, and d 
the distance between the two poles. In deducing the 
formula for Z we have assumed the polar surfaces to be 
two parallel planes, but it can be proved that the same 
law holds good for surfaces of any shape, provided that 
their distance is very small as compared to their area. 
We can therefore apply the formula to the case of a 
cylindrical polar cavity partly filled by a cylindrical 
armature. Here we have two air spaces, and the polar 
surface S is the product of length of armature, b and the 
arc spanned by either pole, K Let J be the distance 
between the polar surface of the magnets and the ex- 
ternal surface of the armature core, and let X represent 
the exciting power producing Z lines, then the above for- 
mula becomes 



X 

2-i 



Z=A 24) 



4 7T * b 



The strength of the field is represented by the quotient 
of exciting power, and an expression which is of the 
character length divided by area. The analogy with 



120 ELECTRIC TRANSMISSION OF ENERGY. 

Ohm's law will be obvious. The electrical resistance 
of a conductor is found by multiplying its specific elec- 
trical resistance with the length, and dividing by the 
area of the wire. In the same manner the magnetic 

resistance of the air space is found by multiplying — - 

with the length (2 £), and dividing by the area (* b) of 

the air space. We can therefore regard - — as the 

4 7T 

specific magnetic resistance of air. The expression 24) 
gives the field in absolute lines ; to obtain it in such 
measure as to be directly applicable for the determina- 
tion of electro-motive force by equation 5) we must 
divide by 6,000. If for convenience we also use inches 
instead of centimeters in the dimensions 3; * and b and 
Ampere turns, instead of exciting power in absolute 
measure we find 

Z= 1880 2J 24a 

Kb' 

This formula is only correct under the supposition that 
there be no other resistance in the magnetic circuit but 
that of the interpolar air space, and that this space be really 
filled with air, and not with some other material. Mate- 
rials differ in regard to the resistance they offer to the 
passage of lines of force, or as it may also be expressed in 
regard to the degree to which they are permeable to mag- 
netic lines of force. Iron is more permeable than nickel 
or cobalt, and these metals are more permeable than 
copper, whilst copper again is more permeable than air. 
The magnetic permeability of any substance can there- 
fore, be expressed by a coefficient ^, which denotes its 



STRENGTH OF FIELD. 121 

relation to the permeability of air, which latter is taken 
as 1. The equation 24) is valid for a space filled with 
air or any other substance having permeability 1, but if 
the space were filled with a substance having permeability 
(jl, the total flux of lines would be given by 

Z =^ 2 «)- 

4 nhb 

We have obtained equations 24) and 24S) by considering 
what flux will be produced across the interpolar space of 
a dynamo, but it is obvious that these formulas have a 
much wider application. Nothing prevents us, for in- 
stance, to apply the formula to the iron of the armature 
itself. For this purpose we need only replace the area 
*b by the cross-sectional area of the iron in the armature 
A ai and the length of path 2£ by the length of path Z a , 
which the lines of force take in flowing across the arma- 
ture core. Then if we know (m the formula will give us 
the flux produced by the exciting power X a , supposing 
none of the other parts of the magnetic circuit to oppose 
the flux ; or the formula may be used to determine the 
exciting power required to drive a given flux Z a through 
the armature. In like manner can we calculate the 
exciting power X m required to drive a given flux Z m 
through the magnets, and by adding these exciting 
powers we arrive at the total exciting power required for 
the whole magnetic circuit. 

The expression 246) may thus also be used in the form 

1 T 

x = ~z 



I* \4ttA 

if Xhe desired in absolute measure. If we wish to ob- 
tain X in ampere turns we would have 



122 



ELECTRIC TRANSMISSION OF ENERGY. 



x=l^z L 



V* 



1-256 A 



p A 



25), 



or, if Z be given in English measure and the dimensions 
in inches : 



v 1880 Z T 

(A. A 



25a). 



The total exciting power required to produce a flux Z a 

Fig. 53. 




through the armature and Z m through the magnets in 
such a machine as that diagramatically shown in Fig. 53 
would therefore be in C.Gr.S. measure: 

Or, X= 1880 § 2 * + ^ f I + ^i° fsZ . . 26a), 

in English measure. 

In a double horse-shoe machine such as Fig. 54 the 



STRENGTH OF FIELD. 



123 



same formulas apply, but only half the total fluxes must 
be inserted, since we have now two magnetic circuits, 
each carrying half the lines which produce the E.M.F. 
It will be noticed that in these equations different sym- 
bols are used to denote the total flux through magnets 
and armature. This is necessary because the two are 
never equal. The flux is produced within the magnet 
cores and is forced across the armature. In this process 
of forcing some lines escape laterally and never pass 
through the armature at all, so that Z m > Z a . This 

Fig. 54. 




point, which is technically termed magnetic leakage, will 
be dealt with presently. 

To apply either of these formulas it is of course 
necessary that we know the value of ^ in each case. 
Now this is is not a constant but varies with the induc- 
tion (number of C.G.S. lines per square centimetre or 
number of English lines per square inch) passing through 
the material. The induction is the ratio of total flux to 

area —: and this is generally denoted by the symbol B. 

Formula 25) may therefore also be written thus : 



124 ELECTRIC TRANSMISSION OF ENERGT. 

X=^-BL, Or,f = -B. 

The ratio y denotes obviously the number of ampere 

turns required per centimetre of path, in order to produce 
the induction B in the material. If we know the per- 
meability corresponding to any induction we can then 
calculate the ampere turns per centimetre or inch of path, 
and therefore the total ampere turns corresponding to 
each part of the circuit for various values of the induc- 
tion. The permeability as a function of the induction 
must of course be determined experimentally for the 
particular type of iron used in the construction of arma- 
ture core or field magnet. It would exceed the scope of 
this book to describe such experiments and the apparatus 
required for them in detail. Suffice it to say that instru- 
ments for determining the magnetic qualities of samples 
of iron have been made and used by Ewing, Hopkinson, 
Thompson, the author, and others. In working with 
such instruments the permeability is not obtained directly, 
but as the ratio of two other quantities, namely, mag- 
netizing force and induction ; and since the magnetizing 

force is given by the expression 'Any- it is from a practi- 
cal point of view more convenient to neglect permeability 
altogether and straightway determine the relation 

X 

between -y, that is, ampere turns per centimetre or inch 

of path, and B, the resulting induction. By plotting 

corresponding values of y and B we obtain for each kind 

of iron a magnetization curve from which we can find at 
a glance how many ampere turns per centimetre or per 



PREDETERMINATION OF CHARACTERISTICS. 125 



inch of path are required to produce a certain induction. 
Figs. 55 and 56 show such curves obtained with samples 
of cast iron, ordinary wrought iron, and special cast steel. 
Fig. 55 gives ampere turns per inch of path when the 
induction is given in English measure. Fig. 56 gives 
ampere turns per centimetre of path when the induction is 
given in C.G.S. measure. To find the exciting power 
required to produce any given flux of lines through the 
armature we must therefore proceed in the following 
manner. We find from the drawing of the machine the 



Fig. 55, 









S 

































— 








*~J 
































, . 


* 


// 


/ 




































/ 


f 






































/ 








































/ 






J^ 


































/ 


/ 


S 




































// 


/ 






































Y 










A 


Tipe 


r*e ti 


zrru 


r p& 


" in 


ch. 



















20 <x> eo eo wo izo i<w 760 iso 200 

C '- Cast Irorv 
J ' . IVhnightJrari 
S . Special Cast Steel 

cross-sectional area and the length of the various parts of 
the circuit, namely, armature core, air space, pole pieces, 
magnet cores, and yoke. Knowing the total flux and the 
area in each case we find the induction in each part of the 
circuit and by reference to such a curve as Fig. 55 or Fig. 
56, the exciting power required 1 for each part. By adding 



1 In the third edition of this book an approximate method for deter- 
mining the exciting power was given which differed from the present and 
exact method in this, that instead of using an actual magnetization curve, 



126 



ELECTRIC TRANSMISSION OF ENERGY. 



up we find the total exciting power required to produce 
the given flux through the armature. In this manner we 
proceed, assuming various values for the useful flux through 
the armature, and determining the total exciting power 
corresponding to each. By plotting these values (Z a on 
the vertical and X on the horizontal) we obtain a curve 
of magnetization for the particular machine under con- 



16.00O 
14.000 
12.000 
70.000 
8.000 
6000 
<hOOQ 
2.000 
O 















Fig 


. 56 
















































— = 








j$L 
























L ■ 


*\ 


V 


s^ 


«/ 




























/ 




































































^£_ 






























































' 




































Airq. 


we 


tUTi 


ISJ 


er i 


erdi 


met 


*e 











10 



zo 



so 



30 <W 

C. Cast Iron 
J". IVhought Iron 
4?. SpeaaL Cast Steel 



eo 



70 



&o 



sideration. Conversely if it be desired to design a machine 
having a certain curve of magnetization we can do so by 



the relation between exciting power and induction was assumed to be pro- 
portional to the ratio tan ( - ^ \ / - - where /3 represented the maximum 

value of B which the iron was capable of attaining under an excessively 
great magnetizing force ; in other words, the number of lines per square 
inch at saturation. When applied within the working range of dynamos 
this formula gave fairly accurate results, and was convenient because in 
the early days of dynamo building very few manufacturers had the neces- 
sary appliances for determining the magnetization curve of the iron they 
used, whereas the point of saturation could be easily found by experiment- 
ing with finished machines. Now, however, that instruments for magnetic 
tests of iron samples of such simple construction as to be fitted for the 
workshop have become available, the method of design given in the text ia 
the one generally adopted. 



PREDETERMINATION OF CHARACTERISTICS. 127 

starting with a preliminary design, and then see what 
alterations in dimension and winding are required to pro- 
duce the desired result. Fig. 57 shows the magnetization 
curve for a machine of the following dimensions : Arma- 
ture smooth ring ; discs, 18 in. diameter, 14 in. long, 3^in. 
deep ; length of polar arc * = 23 in. ; air gap £= *9 in. ; 
mean length of path through armature core 16 in. ; mag- 
nets of the double horse-shoe type, each limb 65 sq. in. in 



Fig. 57. 





S.OOO 
















































































































ueo 


























































s 






























































































































/ 






















fp 




/ 






















f 




/ 






















03 


Soo 


/ 
























/ 


{■ 






















!* 


/ 
























/ 


























/ 


























/ 


19 


m 


u 


t»e 


St 


«M 


u 


?:£_ 


if 


°Q.t 





\ X /m CUftvfc-^T-e • tvfrw* 



section ; length of path through magnet limbs and yoke 
66 in. 

Before proceeding to show how the magnetization curve, 
sometimes also called characteristic of magnetization, 
may be used to determine the actual working condition 
of the machine, it is necessary to say a few words on 
the question of magnetic leakage already mentioned 
a few pages back. It was then pointed out that the 
flux is forced round the magnetic circuit, and that 



128 ELECTRIC TRANS3IISSI0N OF ENERGY. 

part of the flux escapes laterally. The pole pieces of 
the machine send lines through the armature, but at 
the same time they send lines through the air in the 
same way as does an ordinary magnet (Fig. 1). There 
is no means of insulating a surface, so as to prevent the 
dissipation of lines from it ; there must always be a 
certain amount of flux, not only from one pole piece to 
the other through the air, but also between pole pieces 
and magnet cores, bedplate and yoke. In fact, magnetic 
leakage takes place between any surfaces on a machine 
where these are under different magnetic pressure, just 
as in a system of electric conductors immersed in a 
badly conducting liquid, there must be leakage of electric 
current between any parts which are under different 
electric pressure. The magnetic pressure, or in other 
words, the line integral of magnetic force, is of course 
proportional to the exciting power, and where the leakage 
takes place through air (permeability of medium being 
unity), the amount of flux lost by leakage must obviously 
be proportional to the exciting power. If we know the 
position and extent of the surfaces between which leakage 
takes place, it is possible in certain simple cases to cal- 
culate the amount of leakage ; but in most dynamos or 
motors the disposition of the surfaces, and the variation 
of magnetic pressure between them, are so complex that 
an exact determination of the leakage is almost impos- 
sible. Great exactitude is, however, not required, and 
we may for practical work be satisfied with an approxi- 
mate determination. In a completed machine the leakage 
can, of course, be found experimentally by the use of an 
exploring coil and ballistic galvanometer. Suppose we 
have done this with one particular machine, and wish 
to utilize the result for the predetermination of the 



LEAKAGE FIELD. 129 

leakage to be expected in another machine of the same 
type, but different dimensions. Since by far the largest 
part of the total exciting power is required on account of 
the magnetic resistance of the air gap between polar 
surfaces and armature surface, we may take Xa as the 
ampere turns to which the total leakage will be propor- 
tional. The total flux lost by leakage will therefore be 
proportional to the quotient Xa, divided by the average 
magnetic resistance of the leakage paths. Now assume 
that the new machine has every way twice the linear 
dimensions of the machine experimented upon. If we 
imagine in both machines the whole leakage field mapped 
out and similarly divided into small sections then the 
length of path of each section in the large machine will 
be twice that of the corresponding section in the small 
machine, and the areas between corresponding points 
will be as 4 to 1. Since the magnetic resistance of any 
path in air is proportional to the length divided by the 
cross sectional area, the average magnetic resistance of 
the large to that of the small machine will be as \ to 1, 
or in other words, the resistance of the leakage field of 
the large machine will be half that of the small machine, 
and if the ratio of linear dimensions instead of 2 to 1, had 
been 3 to 1, or u to 1, the leakage resistance would be 
one-third, or one-nth that of the small machine. A con- 
venient way of defining the linear dimensions of a 
machine is to give the diameter and length of the arma- 
ture. If the different machines of the same type were 
precisely similar in all respects, either the diameter or 
the length of the armature alone might be introduced 
into the formula for the leakage ; but as there may 
between different machines be variations in the ratio of 
length and diameter of armature, it is convenient to 

K 



130 ELECTRIC TRANSMISSION OF ENERGY. 

assume that their linear dimensions are determined not 
by either alone, but by the square root of their product. 
Thus, if d and I represent diameter and length of the 
armature, we assume that the magnetic resistance of the 
leakage field is proportional to l/\/d I. Its absolute 
value is : 

K 

?=wm '■.-■•■; (27 

where K is a co-efficient, depending on the particular 
type of machine under consideration. For machines of 
the type shown in Figs. 30 and 39, this co-efficient may 
be taken at *21 in cgs., or 460 in English measure. For 
double horse-shoe fields (Figs. 29, 30, 41), -25 and 550 
respectively ; and for upright machines, like Figs. 40, 
•29 and 680. The leakage resistance of multipolar 
machines of the type shown in Fig. 48, can be found by 
reducing the design to an equivalent two pole field. 
Thus, if the machine have 6 poles and an armature 
36 inches in diameter, the d to be inserted in the formula 
for p is not 36, but 36/3 = 12, the diameter being reduced 
in the ratio of the number of pairs of poles. The co- 
efficient K may in this case be taken as for overtype 
machines, namely, *29 in cgs., and 680 in English measure. 
Having thus determined p, we find the total flux lost 
by leakage, 

Xoc 
*=—■.-. . . (28 

P 
Strictly speaking, the formula is only valid as long as 
no current flows through the armature. If the machine 
is at work, the current flowing through the armature 
conductors between the pole pieces of opposite sign, 
assists the field excitation on one side, and opposes it on 



MULTIPOLAR FIELD MAGNETS. 131 

the other side of the brush, the latter effect being the 
greater, so that the magnetic pressure between the pole 
pieces is slightly greater than corresponds to the theo- 
retical value of Xa. The corrections required on this 
account is, however, very small, and may in most cases 
be neglected. The flux through the field magnets can 

now be found by 

Zm = Za + f , 

and this is the value to be used in formulas 26) and 
26 a). 

The investigation above given is sufficient to enable 
the reader to understand the design and working of two 
pole dynamos or motors ; but it is now necessary to make 
a slight extension of the theory, in order to include 
multipolar machines, especially since the latter are gene- 
rally used in transmission plant, where the power to be 
dealt with is considerable. 

Imagine a ring-wound armature taken out of its own 
two pole field, and placed in a four-poled field, such as 
Fig. 48. If the flux emanating from one pole piece be 
the same in either case, and if the speed of rotation be 
also the same, it will be obvious that the E.M.F. gene- 
rated in one quarter of the winding when the armature 
is rotated in the four-pole field, must be exactly equal to 
the E.M.F. generated in one-half the winding when the 
armature is rotated in the two-pole field, for we have in 
either case the same number of lines cut by the same 
number of wires at the same speed. The only difference 
is that, whereas in the two-pole machine the current 
splits into two circuits when passing through the arma- 
ture, in the four-pole machine it splits into four 
circuits, requiring the use of four instead of two brushes. 
With the same current in each armature wire in both 



132 



ELECTRIC TRANSMISSION OF ENERGY. 



cases the total current obtainable from the four-pole 
machine will therefore be double that of the two-pole 
machine. Similarly a six -pole machine will give three 
times, and an eight-pole machine four times the current, 
the E.M.F. being in all cases the same. 

The number of brushes to be used is, in these cases, 
equal to the number of poles in the field ; but by a slight 
addition to the winding of the armature, we are able to 
reduce the number of brushes in all cases to two only. 
This addition consists in cross connections between 

Fig. 58. 




diametrically opposite coils, as shown in the left-hand 
side of Fig. 58 for a four-pole machine. 

We have seen that by increasing the number of field 
poles the output of the machine is proportionately in- 
creased, the increase being in the shape of a larger 
current at the original voltage. It is, however, also 
possible to obtain the increase of output in the shape of 
higher voltage with the original current, and for this 
purpose the winding of the armature must be so altered 
as to bring a larger number of armature coils into series 
connection. Several methods of winding have been de- 



SERIES RING WINDING. 133 

vised, and as an example may be taken that shown in the 
right-hand diagram of Fig. 58. For clearness of illus- 
tration only eleven armature coils are shown, but it will 
be understood that this method of winding is applicable 
to four-pole machines, and ring armatures with any other 
odd number of coils. One end of each coil is connected 
to its commutator plate, and the other is brought round 
to the opposite side, and attached to the wire which 
connects the opposite coil to the corresponding commu- 
tator plate. Thus, the front end of 1 is connected to the 
back end of 2, and to plate 2 of the commutator ; the 
front end of 2 is connected to the back end of 3, and to 
plate 3, and so on, the last connection being the front 
end of 11 to the back end of 1, and to plate 1. The 
current entering the armature at the negative brush, 
where it touches plate 6, splits into two circuits, one 
going round coil 6, up on the outside of the armature, 
the other round coil 5, down on the outside of the arma- 
ture. The former current goes successively up in 7, 8, 
and 9, leaving the armature at plate 10 by the positive 
brush, w r hilst the latter goes successively down in 5, 4, 3, 
2, 1, and 11, leaving the armature also at plate 10. If 
there were 103 coils instead of only 11, the current would 
go similarly up in 50 coils and down in 53, and by follow- 
ing the direction of the current in the diagram, it will be 
seen that it coincides with the direction of E.M.F. in- 
duced in each coil ; in other words, that the E.M.F. 
created by one pair of poles is added to that created by 
the other pair. 

The armature windings up to the present described 
belong to the ring type, the characteristic feature of 
which is, that the wire is brought through the internal 
space of the armature ; this part of the winding acting 



134 ELECTRIC TRANSMISSION OF ENERGY. 

merely as a conductor, and not assisting in the produc- 
tion of E.M.F. It is, however, also possible to wind 
multipolar armatures drum fashion when no conductors 
at all pass through the interior of the armature coil, the 
connection being made entirely at the ends. Diagrams 
for this kind of winding and for two pole machines have 
already been given in Figs. 18 and 19, and it will be 
easily seen how the system may be extended to multi- 
polar machines. In this case the end connections are 
arranged to span not half the circumference, but a 
quarter or a sixth part of it, accordingly as the field has 
four or six poles ; and the winding may be arranged 
either for parallel or for series connection, accordingly as 
it is desired to obtain a larger current or a larger E.M.F. 
In the former case the formulas for E.M.F. previously 
given, are directly applicable ; in the latter case the 
right-hand side of the equation — 4) or 5) — must be multi- 
plied by a number equal to the number of pairs of poles 
in the field. Thus in a four-pole machine the multiplier 
would be two, in a six-pole machine it would be three, 
and so on. 

An inspection of formula 26 will show why, as already 
mentioned in the beginning of Chapter III., small motors 
sometimes fail to act as dynamos. In very small machines 
the air-space £ can, for mechanical reasons, not be re- 
duced in exact proportion with the linear dimensions, and 
the first term on the right-hand side of the equation 
becomes comparatively large. In other words, the mag- 
netic resistance of the air-space is high, and requires a 
correspondingly high exciting power. To produce this 
high exciting power, an amount of electrical energy is 
required, which may exceed the total output obtainable 
from the armature, and if this be the case the machine 



CHARACTERISTIC CURVES. 135 

will fail to excite itself. When the machine is used as a 
motor, this cannot happen, the supply of energy for field 
excitation being from an outside source, the power of the 
armature is not affected thereby. 

It has already been shown how the relation between 
exciting power and field can be graphically represented 
(see Fig. 57) ; and since for constant speed the E.M.F. 
is proportional to the field strength, it is also possible to 
represent by a similar curve the relation between field- 
strength and E.M.F. The exact shape of the curve 
depends, of course, on the construction of the machine, 
showing, so to speak, its general character. On this 
account the name " characteristic curve " has been given 
to any curve which illustrates the relation between two 
of the variable quantities concerned in the working of 
the machine, if all the other quantities are kept constant. 
For instance, if we keep the speed and the current in 
the external circuit constant, we can represent the 
E.M.F. as a function of the exciting power, or in a 
series machine as a function of the current. At constant 
excitation and constant speed, the current can be repre- 
sented as a function of the external resistance. Or the 
torque in a motor for constant current may be repre- 
sented as a function of the exciting current, and so on ; 
the various relations between current, E.M.F. excitation, 
speed, torque, horse-power, and efficiency, can all be re- 
presented graphically by characteristic curves. 

The characteristic curves of magnetisation give, as 
already stated, the total flow of lines of force through the 
armature, provided no other exciting power except that 
applied to the field magnets is active. This condition is 
fulfilled if the field magnets are separately excited, and 
no current is allowed to flow through the armature, the 



136 ELECTRIC TRANSMISSION OF ENERGY. 

electro-motive force in which is in this case exactly the 
same as that which can be measured at the brushes. When 
a current is allowed to flow through the armature, the 
electro-motive force which we measure at the brushes is 
not exactly the same as that generated in the armature, 
but either smaller or larger, accordingly as the machine 
is used as a dynamo or motor. We have thus to dis- 
tinguish between three conditions of working, namely 
(1) no current, (2) dynamo current, and (3) motor current 
passing through the armature. The first condition can be 
obtained by simply opening the external circuit, but we 
can also imagine that the external circuit remains closed, 
and that some source of electro-motive force is inserted, 
acting in opposition to the electro-motive force gene- 
rated in the armature, and that this is so accurately 
adjusted as to prevent a flow of current in either direc- 
tion. We shall then have, so to speak, a static balance 
between the armature and opposing electro-motive force. 
And for this reason the author has suggested the name 
" static characteristic " to any characteristic curve repre- 
senting this condition of working. If we now imagine 
the opposing electro-motive force reduced, it will no 
more be able to balance the electro-motive force of the 
armature, but will be overpowered by the latter, with 
the result that a current will flow, doing work upon the 
opposing electro-motive force. The machine now works 
as a dynamo, absorbing mechanical and giving out 
electric energy. Any characteristic curve expressing this 
condition of working, we call " dynamic characteristic." 
If, on the other hand, we increase the opposing electro- 
motive force until the latter overpowers the armature 
electro-motive force, a current will be forced through the 
armature doing work in overcoming its electro-motive 



STATIC, DYNAMIC AND MOTOR CHARACTERISTICS. 137 

force, in other words driving the machine as a motor. 
Any characteristic expressing this condition of working 
of a machine we call " motor characteristic." For certain 
reasons which will be given presently, the dynamic cha- 
racteristic must always be lower than the static cha- 
racteristic, and the same holds good generally for the 
motor characteristic, but there are cases when the motor 
curve lies above the static curve. Confining ourselves 
for the present to dynamos only, it is easy to see why 
the dynamic curve must be below the static curve. 
Allowances must in the first place be made for the drop 
in electro- motive force due to the electrical resistance of 
the armature. This drop can of course be calculated by 
multiplying current and resistance. But beyond this, 
there is a further reduction of electro-motive force, 
which can be explained as follows. Let us for the 
moment assume that we work a two-pole dynamo with 
the brushes set exactly at right angles to the polar 
diameter, and let us concentrate our attention on say the 
positive brush, that is the brush where the current leaves 
the armature. In all the coils on one side of this brush 
the current flows in one direction, say towards the com- 
mutator on the outside of the armature, whilst in all the 
coils on the other side of the brush it flows in the oppo- 
site direction. There is thus a reversal of current in 
each coil as it passes under the brush. Whilst under 
the brush, the coil is short circuited on itself, but as a 
moment before it was traversed by half the total arma- 
ture current, there will remain some current flowing 
during its period of short-circuiting by virtue of the self- 
induction of the coil. This current becomes gradually 
weaker, owing to the resistance of the coil, but even if 
this cause were sufficient to bring the current to zero, it 



138 ELECTRIC TRANSMISSION OF ENERGY. 

can obviously not reverse it. By the time the coil 
emerges from under the brush, the previous current in it 
may or may not yet have died out, but at that instant half 
the total armature current is forced through it in the 
opposite direction. This causes a violent spark, which can 
only be avoided by shifting the brush into a more ad- 
vanced position. When in that position, the coil whilst 
under the brush cuts through lines of force which induce 
in it an electro-motive force opposed to the persisting 
current, and bring it thus quickly to zero. But these 
lines of force do more ; they start the current in the 
opposite direction, so that the coil at the moment of 
emerging from under the brush carries already the same 
current as will be forced through it afterwards, whereby 
the transition from the idle, short-circuited position under 
the brush to the working position beyond the brush, 
takes place quite gradually and without sparking. By 
shifting the brush forward we have killed out the spark, 
but we have sacrificed some of the lines of force which 
might otherwise have increased the electro-motive force 
of the armature, and which, whilst the machine was 
working on open circuit, have indeed been so utilized. 
There are therefore more lines of force utilized whilst 
the machine is working statically, than whilst it is work- 
ing dynamically, from which it follows that the dynamic 
electro-motive force must be lower than the static electro- 
motive force. A further reduction of electro-motive 
force is due to the fact, thet the armature itself becomes 
magnetised by the current flowing through its coils, and 
reacts on the field magnets. If it were possible to work 
with the brushes on the neutral diameter, the poles 
developed in the armature would stand exactly midway 
between the main field poles, and would neither strengthen 



ARMATURE REACTION. 



139 



nor weaken them, but the brushes must for the reason 
already given be shifted forward, which brings armature 
and field poles of the same sign nearer together, and the 
result is, that the main field is somewhat weakened, 
which again reduces the electro-motive force. In reality, 
the phenomena here briefly sketched, and which are 
technically comprised under the term " armature reac- 
tion," are not quite as simple as here stated, but it would 



Fig. 59, 



Volts. 
80 



70 
60 















/ 




























050 


Reus. 










































\ 




Amp 


eres. 







50 
40 
30 
20 
10 



10 20 30 40 50 60. 
INTERNAL CHARACTERISTIC OF A GRAMME DYNAMO. 

exceed the scope of the present work to enter more fully 
into details, the- more so as the total effect of armature 
reaction is in good dynamos very small, amounting often 
to less than five per cent, of the total electro-motive 
force. In badly designed machines it may become con- 
siderable, as can be seen from Fig. 59, which represents 
the internal characteristic of an A gramme dynamo, 
tested by M. Marcel Deprez. 

This behaviour of the dynamo can best be studied with 



140 



ELECTRIC TRANSMISSION OF ENERGY. 



separately excited machines, and Mr. Esson has made 
very careful trials on the subject, which were published 
in April, 1884, in " The Electrical Review." The dy- 
namo experimented upon was a " Phoenix " machine with 
Pacinotti armature. It was separately excited and kept 
running at a constant speed of 1,600 revolutions a minute, 
whilst the current which was permitted to flow through 
the armature was varied by means of a rheostat. The 

Fig. 60. 



60 


v.^ 










50 
40 




















Eb 










\ 


30 


CO 








eV 


2* 


n 


WO Reus 






20 












10 







Amperes 







u 10 20 30 40 50 

EXPERIMENT WITH PHCENIX DYNAMO. 

line E, Fig. 60, represents the internal electro-motive 
force corresponding to the constant exciting power if there 
were no reactions. The line Eb represents the electro- 
motive force which would be found at the brushes if 
there were no reaction, and the line Eb 1 was that actually 
observed. The difference of the ordinates of Eb and Eb 1 
represents the loss of electro-motive force due to self- 
induction, weakening and distorting of the field. 

The armature reaction in a motor is very similar to 



MOTOR CHARACTERISTICS. 141 

that in a dynamo, except that the electro-motive force 
lost in resistance must be added to, instead of sub- 
tracted from the internal armature electro-motive force. 
If the machine is properly constructed, there will there- 
fore be very little difference between its dynamic and 
motor characteristics/ both lying below the static cha- 
racteristic, but if the machine is not so constructed as to 
give a high efficiency, then it may happen that its motor 
curve is considerably higher than its dynamic, and even 
higher than its static curve. The reason is obvious. If 
a sensible amount of energy is wasted in eddy currents or 
hysteresis, this energy must be supplied by the motor 
current in the shape of an increased terminal pressure. 
Now we find the motor characteristic of electro-motive 
force by deducting from the electro-motive force at the 
brushes which can be measured, the calculated electro- 
motive force necessary to overcome the resistance of the 
armature. The latter being constant, it follows that the 
higher the brush electro-motive force, the higher must 
also be the motor electro-motive force. The author has 
verified this conclusion by testing a Burgin machine as a 
dynamo and as a motor. As was to be expected, the 
dynamic curve was found to lie below the static curve, 
but the motor curve, instead of being below the static 
curve, was found to lie above it. The reason is probably 
that eddy currents in the corners of the iron wire hexa- 
gons which form the armature core, and a certain amount 
of surging of lines over the surface of the pole pieces pro- 
duced by these corners, absorb a sensible amount of 
energy requiring an increased electro-motive force in the 



1 If the loss of E.M.F. due to armature reaction is made equal to the 
loss of E.M.F. resulting from armature resistance we obtain a motor which 
will run with practically constant speed under a varying load, 



142 ELECTRIC TRANSMISSION OF ENERGY. 

driving current, and thus making it appear as if the 
counter electro-motive force in the armature were higher 
than it really is. The fact that some machines show a 
high counter electro-motive force, has led certain scientists, 
and notably Professors Ayrton and Perry, to formulate 
a theory of electro-motors, according to which the arma- 
ture was credited with some sort of power to increase the 
strength of the field instead of weakening it, as is actually 
the case, and it was recommended that motors should 
have small field-magnets and large armatures. Practical 
experience has, however, disproved this theory, and the 
best motors are nowadays designed by the use of the 
same formulae as the best dynamos. 

We may now proceed to show the use and interpreta- 
tion of characteristic curves generally. 

Fig. 61 shows the internal and external characteristics 
of a series-wound Siemens dynamo, as given by Dr. Hop- 
kinson in the Proceedings of the Institution of Me- 
chanical Engineers, 1879. The dotted curve O JE„ repre- 
sents the electro-motive force at the terminals of the 
machine, and the curve shown in a full line O E a , that in 
the armature. The latter is obtained from the former by 
adding to its ordinates the internal losses of electro-motive 
force due to armature reaction and resistance. This can 
be represented roughly as the product of current and a 
certain resistance, which latter was in that particular 
machine 0*6 ohms. Thus at 50 amperes the loss is 30 volts, 
and it will be seen from the diagram that the difference 
between the two ordinates corresponding to 50 on the 
abscissae is 30. We can also represent the loss of electro- 
motive force by a characteristic, and since it is always pro- 
portional to the current, the characteristic in this instance 
becomes a straight line, O r. The geometrical tangent 



HORSE-POWER CURVES. 



143 



of the angle which this line forms with the horizontal 
is evidently equal to the resistance in question. The 
ordinates enclosed between O r and O E ai represent the 
external electro-motive forces, and therefore the internal 



Volts 
100 



90 



80 



70 



60 



50 



40 



30 



20 



10 



Fig. 61, 



- ; 




\ 


\ \ 


\ 


\^ 


— ^Ea 










\ 


\ ' 


'% 




' 


c^/ \ 


'« 


\ 


^ ^ 


\ 






\.'-"~ 


■ - «»._ 


^ 
A 

"*"-\. 


\ 








\ 


\ 




\ ""*^ 


Et\ 




/ i 

I \ 
1 \ 




> 


^- 


x 


X 


/ / 


1 \ 


% 




-^ 


N< 


^., 


it 










**** 


*„. 


1 


> 


y 






---... 



















10 20 30 40 50 60 70 Amperes 

CHARACTERISTICS OP SIEMENS DYNAMO. 



characteristic, O JE a9 becomes the external characteristic 
if we take O r for the base line instead of the horizontal. 
By a very ingenious method due to Professor Silvanus 
P. Thompson these characteristics can also be used to 
show at a glance the horse-power which corresponds to 



144 ELECTRIC TRANSMISSION OF ENERGY. 

any particular current or electro-motive force. As already 

shown the horse-power represented by a current c flowing 

c E . 
under an electro-motive force E a is H-P = H * One 

746 

horse-power can be represented by an infinite variety of 
c and E a , but these values must all satisfy the equation 

746 = c E a . 
A curve representing one-horse power w T ill pass through 
all such points of w4iich the product of their ordinates 
is a constant, viz., 746. Similarly a curve representing 
the value of two horse-power will pass through points 
of which the product of their ordinates equals 1492, and 
so on. In other words, all the horse-power curves are rect- 
angular hyperbolas, 1 and by drawing a set of these curves 
across our diagram — as shown in dotted lines — we can 
determine at a glance what is the horse-power correspond- 
ing to any point on the characteristic. Thus a current 
of 30 amperes represents about 3*35 H-P of internal elec- 
trical energy, and about 2*7 H-P of electrical output or 
energy delivered into the external circuit. A current of 
50 amperes represents a little over 6 H-P internal, and a 
little over 4 H-P external energy, and so on. 

In a dynamo the internal characteristic lies always 
above the external characteristic. In a motor, however, 
their position is reversed, since the external electro-motive 
force must necessarily be greater than the counter-electro- 
motive force developed in the armature coils. Fig. 62 
shows the characteristics of the Siemens dynamo men- 
tioned above if used as motor. 'Not to get the diagram 
too long the speed has been reduced to 500 Revolutions. 
The curve O E a represents the counter electro-motive 

1 The scales for volts and amperes being equal. 



SPEED CHARACTERISTICS. 145 

force developed in the armature coils, and the curve OE„ 
which is shown in a dotted line, represents the terminal 
electro-motive force. The difference between the ordinates 
of the two curves represents the electro-motive force 
necessary to overcome the internal resistance of the 
machine. By drawing the straight line O r under an 
angle, the tangent of which is numerically equal to the 
internal resistance, but this time below the horizontal and 
not above it as in the former example, we can regard it 
as the new base line, and then the curve O E a becomes 
the external characteristic. 

In diagram (Fig. 62) it is assumed that by some means 
we keep the speed constantly at 500 revs, a minute. Easy 
as it is to fulfil such a condition in a dynamo, it presents 
considerable difficulties if we have to deal with a series- 
wound motor, because its speed depends on a number of 
factors which to a certain extent may vary independently 
of each other. The speed depends on the current and 
electro-motive force supplied to the motor, and on the 
amount of mechanical work it has to do. In some cases 
the work itself, that is the product of turning moment 
and speed, depends on the latter, and thus it will be seen 
that the relation between these various quantities is of a 
rather complex nature. It is however easy to represent 
these relations graphically by the use of speed charac- 
teristics, which were first published by the author in " The 
Electrician," of December 29th, 1883. Assume the case 
that the external electro-motive force is a fixed and con- 
stant quantity. What will be the relation between speed, 
power, and efficiency of, say, a series-wound motor? 
Since E t is constant at all currents, we have practically 
an unlimited supply of current such as would be ob- 
tained from the mains in a system of town supply. The 

L 



146 ELECTRIC TRANSMISSION OF ENERGY. 

current passing through the motor will depend on its 

Fig. 62. 



inn Volts 









\ 


\ 


\ 








\ 


X \ 


\ 


90 








\ 


y \ 








■ 


% / 








» 


\ 


,'\ 








\ 




\ 








\ 


\ / 


\ 








\ 




\ 


80 






\ 


,\ 


\ 






\ 


/ \ 


\ 






\ 


/ 


** 


*i 






, 


/ 




^ 














70 














\ 




\ 


\ 






', 


\ 


\ 


\ 


60 




\ / 


\ 


\ 


•" \ 




\ / 

v / 

\ / 

\ / 




f^ "^\ 








»/ 








50 


























/ / 




'% 


\ 


























40 




/ v - 




\ 






/ \ 




\ 






/ 


/ 


"% 




\ 


30 




























\ 




















» / 




\ 






20 


< / 






X N 




i 1 






*■ 


..^ 




If 








**"--- 


10 


1 1 















10 


20 


30 


40 



Et 



SO Amperes 



CHARACTERISTICS OF SERIES MOTOR. 



resistance, and on its counter-electro-motive force. The 
former is constant, whilst the latter increases with the 



SPEED CHARACTERISTICS, 



147 



speed. The faster we allow the motor to run the less 
current will flow through it, and the less power will be 
absorbed by it. Let in Fig. 63 the speeds be plotted as 
abscissae, and the electrical horse-power absorbed as ordi- 
nates, then with a series-wound motor we obtain the 
curve W W. The exact shape of this curve depends, of 
course, on the construction of the motor, but its general 
character will be as shown. The easiest way of finding 
the curve experimentally is by attaching a brake to the 
motor, and loading it with different weights so as to pro- 
Fig. 63. 




SPEED-CHARACTERISTICS OF SERIES MOTOR. 



duce different speeds. The horse-power absorbed by the 
brake can at the same time be plotted in the curve w w. 
If we begin with an excess of load on the brake, which 
will hold the motor fast, a maximum of current will flow, 
and a maximum of electrical energy will be absorbed 
without producing any external work. On the other 
hand, if we remove the brake altogether the motor will 
attain a maximum velocity o m, and again no external 
work will be produced, but in this case very little current 
will pass, and the electrical energy absorbed will be a 
minimum. Between these extreme limits of no speed and 



148 ELECTRIC TRANSMISSION OF ENERGY. 

maximum speed external work will be produced, and 
there is one particular speed, o a, at which this work will 
be a maximum. The ratio of the ordinates of W and w 
can be plotted in a curve, n y, drawn to any convenient 
scale, and this gives the commercial efficiency of the 
motor as a function of the speed. There is one particular 
speed, o b, at which the efficiency is a maximum, but this 
is not necessarily the same speed as that for which the 
work is a maximum. As a rule it is considerably greater, 
and in actual work the motor should be so geared that 
it runs at or about the speed of maximum efficiency. 

The experimental determination of the most economical 
speed, as just described, requires the employment of a 
dynamometer or brake, and if such an apparatus be not 
at hand, cannot be adopted. In this case a different 
method can be used, which is fairly reliable, although not 
quite so accurate as the actual power test. The question 
to be solved is the relation between speed and current in 
a given series-wound motor supplied with current at a 
constant electro-motive force. This question can be 
solved if we know the internal resistance of the motor 
and its internal characteristic. Having obtained the 
relation between speed and current, we can construct the 
diagram Fig. 63, making a certain allowance for the 
efficiency of conversion. We assume that the motor derives 
its supply of current from a pair of mains between which 
a potential difference of 100 volts is maintained. Let, in 
Fig. 64, O JE a , represent internal characteristic for a con- 
stant speed of say 500 revs., and let the inclined straight 
line, r, be drawn across the diagram at such an angle with 
the horizontal that its geometrical tangent is numerically 
equal to the internal resistance of the motor in ohms, then 
the ordinates of the line, r, represent the counter-electro- 



SPEED CHARACTERISTICS. 149 

motive forces which must be created in the coils of the 
armature so that any given current may pass. Thus, at 
100 amperes, the counter-electro-motive force must be 40 
volts. If the armature revolves at a speed of 500 revo- 
lutions a minute, we see from the characteristic that its 



Fig. 64, 



Volts 



IUU 
90 

80 
70 








































s s 






































































60 

50 

40 

30 

20 

10 



100 

200 

300 

400 

500 

600 

700 

800 

900 






,. 


-- 
































,'' 




































/ 














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\r 


















/ 






















N 














/ 




































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/ 



































Ea. 



Amperes. 



1000 Reus. 
RELATION 



BETWEEN SPEED AND CURRENT IN SERIES-WOUND MOTOR. 



counter-electro-motive force is 68 volts, and to bring the 
latter down to 40 volts, so that a current of 100 amperes 
may pass, the speed will have to be reduced in the pro- 
portion of 68 to 40. The speed corresponding to a cur- 

40 
rent of 100 amperes is therefore 500. — = 294 revolu- 



150 ELECTRIC TRANSMISSION OF ENERGY. 

tions. Similar calculations can be made for other values 
of current, and the speeds obtained can be plotted in 
a curve shown in Fig. 64, below the horizontal. At 166 
amperes the speed is zero, because the whole of the con- 
stant electro-motive-force available of 100 volts is re- 
quired to overcome the internal resistance of the motor, 
leaving nothing to be opposed by counter electro-motive- 
force. At 16 amperes the speed is 1000 revolutions, and 
at smaller currents the speed might be still greater. 
Theoretically, it should be infinite if no current passes, 
and this would be the case if the motor w r ere free to 
revolve without doing any work, and if there were no 
internal mechanical losses. This, of course, is an im- 
possible condition, and a limit is set to the speed by the 
work which must be done to overcome mechanical and 
magnetic friction. In good motors this is, however, com- 
paratively small, and consequently the speed of the motor, 
when running empty, is inconveniently high. This is a 
great drawback in many cases, especially where motors 
are required to drive lathes and other machinery offering 
a variable resistance. The example represented in Fig. 
64, applies also to the case where a series-wound motor is 
worked from a set of secondary cells, having a very low 
internal resistance, as the electro-motive force is then 
approximately constant at all currents. To lessen the 
difference in speed it is usual to insert a rheostat or vari- 
able resistance into the circuit between the cells and the 
motor. A maximum of resistance is inserted when the 
motor is running empty, and as the load increases re- 
sistance is switched out so as to regulate the speed. At 
best this is a clumsy device, requiring personal attention, 
and not very efficient, as with it variations in speed can 
never be altogether avoided. It is also wasteful, the heat 



REGULATING THE SPEED. 151 

developed in the artificial resistance being so much power 
lost. A better plan is to wind the field magnets of 
the motor on the compound principle, both main and 
shunt coils magnetizing in the same direction. This will 
raise the early part of the characteristic as shown in 
dotted lines, and will reduce the speed as shown also in a 
dotted line. This method is not a complete cure for the 
evil, but it is a palliative for it which in practice proves 
very successful. To make the motor perfectly self-regu- 
lating, it would be necessary to let the main coils on the 
field magnet excite the latter in an opposite sense to the 
shunt coils ; but then a very valuable quality of the series 
motor, viz., its great starting power, would be lost. If a 
motor is employed for railway or tramway work it is very 
important that there should be an excess of power at 
starting. This condition is admirably fulfilled by the or- 
dinary series- wound motor, since the current, the strength 
of the field, and the statical effort or torque are all maxima 
when the motor is at rest and decrease as it gathers speed. 
There is thus an automatic adjustment between speed, 
power, and resistance. Take, as an example, an electric 
tramcar worked by accumulators. On a heavy gradient 
or bad part of the road, the speed is low, allowing a large 
current to pass through the motor, thus providing the 
extra amount of tractive force necessary ; on a good level 
road the speed will increase, less current will pass through 
the motor, and less tractive force will be developed. 



CHAPTEE V. 

Graphic Treatment of Problems — Maximum External Energy — Maximum 
Theoretical Efficiency — Determination of best Speed for Maximum Com- 
mercial Efficiency — Variation of Speed in Shunt Motors — The Compound 
Machine as Generator — System of Transmission at Constant Speed — 
Practical Difficulty. 

The treatment of problems relating to the electrical 
transmission of energy is greatly simplified by the use of 
the curves explained in the preceding chapter, and by 
other graphic methods, of which we may mention that 
due to Professor Silvanus Thompson. The problem is 
as follows. Let a square AB C D be drawn so that the 
length of one of the sides shall represent the electro- 
motive force E of the supply to any convenient scale, 
Fig. 65, and let the counter-electro-motive force e of the 
motor be represented by the length A F = A G. Draw 
through F and G the lines F K and G H respectively 
parallel to A B and A C. The energy supplied to the 
motor equals the product of electro-motive force E and 
current C, whilst the work converted into mechanical 
energy in the armature of the motor equals the product of 
counter-electro-motive force e and current C. Let R repre- 

E e 

sent the total resistance in the circuit, then C = — - — • 

Jti 

which in our diagram is represented by the length F C 

divided by R. The energy delivered to the motor is 

evidently 



MAXIMUM COMMERCIAL EFFICIENCY. 

E(E — e) 



153 



R ' 

and that converted in the motor is 

e {E— e) 
R ' 
Now the area of the rectangle F K D C = E (E — e) 
and the area of the rectangle G B K L = e (E — e) ; 
and since R is a constant, we find that these areas — shaded 
in our diagram — are proportional to the work expended 
and recovered. 

Thompson's diagram can immediately be used to solve 

Fig. 65. 




graphically two of the problems which have already been 
treated analytically in the first chapter (page 39). These 
are the following : First, what is the condition of maxi- 
mum work obtained from the motor ? and, secondly, what 
is the condition of maximum efficiency ? 

The answer to the first question is easily found by 
inspecting our diagram, Fig. 65. Since the rectangle 
G B K i, which represents the work of the motor, is 
inscribed between the diagonal A D and the sides A B, 
D B ; the question resolves into that of finding which of 
all possible rectangles inscribed within these lines has a 
maximum of area. This is evidently a square, the sides 



154 ELECTRIC TRANSMISSION OF ENERGY. 

of which are half as long as those of the external square. 
In this case the work expended is represented by a 
rectangle of half the area of the external square, and 
the efficiency is therefore 50 per cent. 

1 f 2 
We have : Work expended — — . 

1 E 2 

„ Work recovered — — . 

E 4 

?v Efficiency n = 0*50. 

As regards the second question it will readily be seen 
that the discrepancy in the area of the two rectangles, 
Fig. 64, is the greater, the nearer the point L is to A, or in 
other words, the smaller the counter-electro-motive force. 
In the same measure as the latter increases, point L is 
pushed further towards D, and the areas of the two rect- 
angles become more and more equal. The efficiency, 
therefore, tends towards unity as the counter-electro- 
motive force of the motor tends towards the electro-motive- 
force of the source of supply of electricity. This state- 
ment has already been made in the first chapter, and it is 
theoretically quite accurate ; but from a practical point 
of view it requires some qualification. It will be seen that 
when the counter-electro-motive force of the motor ap- 
proaches very closely the electro-motive force of the 
supply, the current becomes very small, and the work 
expended and converted becomes also very small. Now 
the work converted in the motor is not all available in 
the shape of external mechanical energy, and it may 
well happen that in this case, after the resistance of 
mechanical and magnetic friction has been overcome, no 
margin remains for useful external work. The com- 
mercial efficiency would therefore be Zero, although the 
theoretical efficiency is a maximum. To put the matter 



MAXIMUM COMMERCIAL EFFICIENCY. 155 

in another way : a certain minimum of current is required 
to overcome the friction of the motor, quite apart from 
any external resistance. It has been shown that with a 
constant field the torque of the motor depends only on 
the current which passes through the armature, and is 
independent of the speed. We may apply this law with 
sufficient approximation to the present case and assume 
that at all speeds the current which is required to over- 
come the internal friction of the motor is constant. Let y 
represent this minimum of current, which will just keep 

the motor alone going, then — — e — y is the current 

doing useful external work, and the commercial effi ciency is 

E-e 



n = e R 



-y 



E E-e 
R 

Ee — e 2 — e Ry 



n = 



E 2 -Ee 

To find the condition under which y\ becomes a maximum 

we put — = and obtain 

{E -e) 2 = E Ry 29). 

This formula is capable of graphic representation. Let 
in Fig. 66 O A represent the current y, which is required to 
keep the motor revolving at or near its normal speed when 
no external work is being done, and let O IT represent the 
electro-motive force E of the source, which we suppose to 
be constant for all conditions. This would be practically 
the case if the source of current were a self-regulating 
dynamo, or a set of secondary batteries having a very low 
internal resistance. The area of the rectangle O AG H 
represents the number of watts required to overcome the 



156 



ELECTRIC TRANSMISSION OF ENERGY. 



friction of the motor at its normal speed when doing no 
external work, and if the motor be shunt-wound, or com- 
pound-wound for constant speed, its strength of field will 
not greatly vary when external work is being done, and 
we may with a reasonable degree of approximation re- 
gard the area of the rectangle O A G Hto represent the 
internal loss of energy in the motor under all conditions. 
Draw O B at such an angle to the horizontal that its 
geometrical tangent is numerically equal to the total 
electrical resistance of the motor and the line, then S A 



e. h 



Fig. 66. 

F 



L T 



N O 



A B 



D 



represents the loss of electro-motive force corresponding 
to the current O A, M D represents the loss correspond- 
ing to the current O D, and so on. Produce O N= S A 
and complete the rectangle O NPH (dotted in the 
diagram). The area of this rectangle is evidently equal 
E i?y, and if w^e produce a square O B K L of equal 
area, the side O L will be equal to the square root of 
E By, and will, according to equation 29, represent E— e. 
Hence it follows that if we so load the motor that its 
counter-electro-motive force e = HL, it will work with 
maximum commercial efficiency. The energy obtained 
at the motor spindle is represented by the area of the 



PRACTICAL EXAMPLE. 157 

rectangle G F M T, the energy expended at the source 
of electricity is represented by the area of the rectangle 
O D F H, and the ratio of the two is the commercial 
efficiency. 

In the preceding chapter it was shown how, by the use 
of an absorption dynamometer, the speed for maximum 
commercial efficiency can be found experimentally ; it 
was also shown how, in the case of a series-wound motor, 
this determination can be made with a fair degree of 
approximation even without the use of a dynamometer. 
We can now employ the relations just found to make this 
determination for shunt or compound-wound motors also, 
without requiring the use of a brake. This may be ex- 
plained by an example from actual practice. One of the 
author's dynamos (shunt-wound and designed to feed sixty 
glow lamps) was used as a motor. The electro-motive 
force of the source, which was a compound-wound dynamo, 
was 100 volts, current through motor when running empty 
was 4 amperes, speed 1,100 revs., and resistance of line and 
armature *2 ohm. We have now By = *8 and V E By = 
V 80 = 8*94. To obtain best efficiency the motor must 
therefore be so speeded that its counter-electro-motive 
force e = 100 - 8'94 

e = 91 volts. 

When running empty the counter-electro-motive force is 
100 - 0-8 = 99-2. 

The best working speed is therefore 

91 
1100.-—- = 1010 revolutions. 

The current passing at that speed is 45 amperes, of which 
4 amperes are required to overcome the internal friction 
of the motor, leaving 41 amperes to produce useful 
external work. By gearing the motor to the speed of 



158 ELECTRIC TRANSMISSION OF ENERGY. 

1010 revolutions a minute, we shall therefore obtain 

41 X 91 

— = 5 '07 H-P, actually available on the motor 

spindle. 

But it is not always possible to keep the motor running 
exactly at the right speed, especially if the load should 
vary, and in this case it becomes important to know how 
far on either side of the best speed a variation may take 
place without seriously reducing the efficiency. For the 
motor above cited we find the following figures : — 
1010 revs. 5-07 H-P. e = 91 c = 45 82-8% Com. effic. 
1065 „ 2-07 „ = 96 = 20 76'7 

944 „ 8-20 „ =85 =75 80'0 „ 

It will be seen from this table that a shunt-wound motor 
is fairly self-regulating, the range of speed between no 
load and full load being only about 15% m the present 
instance. It should be here remarked that the motor de- 
scribed is intended for a working current of 45 amperes, 
and should not be loaded to more than 5 H-P for con- 
tinuous work. This reduces the extreme variation in speed 
to something under 9%. To show the influence of the 
resistance of the armature on the best speed and efficiency, 
a table is added, calculated for the same motor and the 
same electro-motive force, but with an additional resis- 
tance of '3 ohm in the circuit of the armature, making 
R = -5 

950 revs. 2-82 H-P. e = 86 c = 28 73-5% Com. effic. 

860 „ 4-30 „ = 77 = 45 70-5 „ 

1000 „ 1*96 „ = 90 = 20 72-0 „ 

In practice, however, the additional resistance would 
not be placed in the circuit of the armature, but in the 
line, where, indeed, it is unavoidable if the transmission 
of energy has to be made over a considerable distance. 



THE SHUNT MOTOR. 159 

By inserting the resistance into the armature circuit only, 
we have not disturbed the condition under which alone 
formula 29) gives the best speed, viz., that the strength of 
the field shall be the same for all currents and speeds. 
This condition might be fulfilled even in the case of a 
transmission to a considerable distance if we excite the 
field of the motor separately or by a pair of separate wires 
from the distant source, but in practice such an arrange- 
ment would be too complicated and, as we shall see pre- 
sently, it would have no advantage in point of constancy, 
of speed over the simpler plan of exciting the field of our 
shunt-motor direct from the line which brings the working 
current. The effect of an increased resistance in the line 
is in the first instance to lower the electro-motive force at 
the terminals of the motor. With a constant strength of 
field this would naturally lower the speed of the motor, 
but if its field magnets are not excited to the saturation 
point, the reduction of electro-motive force at the ter- 
minals of the motor will result in a reduction of the 
strength of the field, thus allowing more current to pass 
through the armature by which its torque and speed is 
increased until its counter-electro-motive force again 
balances the reduced electro-motive force of the supply. 
The variation of speed will therefore be smaller than 
would at first sight appear. But a little consideration 
will show that the gain in speed due to the increased 
armature current can never quite compensate for the loss 
of speed due to the reduced electro-motive force, and thus 
a pure shunt-wound motor, if fed from a source of con- 
stant electro-motive force can never be perfectly self- 
regulating. It must run faster when the load is thrown 
off, and it must run slower if more work is put on it. 
We found the same to be the case with the pure series- 



160 ELECTRIC TRANSMISSION OF ENERGY. 

wound motor, but in a more marked degree. In this 
respect the shunt motor is preferable, as will be seen from 
the above tables (page 158), as its speed when running 
empty is only slightly higher than when loaded, whereas 
the speed of the series motor when running empty is 
excessive. On the other hand, the shunt motor has no 
starting power, since its armature, when at rest, forms a 
short circuit of very low resistance. To start a shunt 
motor it is necessary to arrange the switch in such manner 
that the field becomes excited before the current is 
allowed to flow through the armature, and to avoid 
excessive sparking or heating of the armature, in cases 
where the motor has to start with the load on, additional 
resistances must be placed into the armature circuit, 
which are again cut out as soon as the motor has attained 
some speed. 

We shall now investigate the problem in what manner 
the electro-motive force of the source of supply must be 
varied in order to produce constant speed in a shunt- 
wound motor working under a varying load. Not to com- 
plicate the problem too much, we assume that the field 
magnets of the motor are, with the normal electro-motive 
force, excited to a very high degree, so that any slight 
variation in the magnetizing current cannot produce any 
material difference in the strength of the field. Under 
this condition the counter-electro-motive force in the 
armature of the motor will vary directly as the speed ; 
and since the latter is to be constant, the former will also 
be constant for all loads. Let y represent the armature 
current if the motor runs without load, let c be the 
current when there is a load, and let e be the constant 
counter-electro-motive force, then (c—y) e represents the 
external mechanical energy ; and since e and y are both 



THE SHUNT MOTOR. 161 

constants, a variation of external energy, or, as we call it, 

a variation in the load of the motor, makes it necessary to 

vary the current c through its armature. This is done by 

raising the electro-motive force E of the supply if the load 

increases, and lowering it if the load decreases. Let R 

E — e 
be the resistance of line and armature, then c = — =— 

xt 

and E = e + c R. We neglect as very small the amount 
of current required for the shunt on the field magnets. 
The equation shows that to maintain a constant speed of 
the motor the electro-motive force of the source ought to 
increase with the load. Its lowest value, when there is 
no load, will be E = e + y R } and its highest value will 
be when load, and consequently current, are both maxima. 
The difference between the lowest and highest value will 
be the less, the smaller the resistance R of line and arma- 
ture, but it can never entirely vanish, for that would re- 
quire a line and an armature of no resistance. From the 
above considerations it will be seen that two shunt-wound 
dynamos can under no circumstances form a system of 
transmission of energy at constant speed of the receiving 
machine, because the electro-motive force of the generator 
— which we suppose to be driven by some prime mover at 
a constant speed — decreases as the current given out in- 
creases, whereas the motor requires exactly the opposite 
relation between these quantities. A shunt motor might 
be made to run at a constant speed by using an over- 
compounded dynamo for the generator. The principle of 
the compound-wound dynamo, or, as it is also called, of 
the self-regulating dynamo, is so well known that a few 
words only of explanation will suffice. 

Let the field magnet of a dynamo machine be wound 
with two coils, one of fine high resistance wire coupled 

M 



162 ELECTRIC TRANSMISSION OF ENERGY. 

direct to the brushes, and the other of stout low resistance 
wire, coupled in series with the brushes and the external 
circuit. If the latter be open, no current passes through 
the main or series coils, and the magnetism of the machine 
is entirely due to the exciting power of the shunt coils. 
If the machine is properly designed, this amount of mag- 
netism should produce an internal electro-motive force 
exactly equal to that which it is desired to maintain at all 
currents in the external circuit, provided the dynamo is 
driven at a constant speed. If a current is permitted to 
flow through the armature, the electro-motive force 
measured at the brushes is naturally somewhat less than 
that created within the armature coils, on account of 
losses through resistance and self-induction, the loss in- 
creasing with the current. To compensate for this loss it 
is necessary to increase the internal electro-motive force, 
and this is accomplished by an increase in the strength of 
the magnetic field. This is brought about automatically 
by the main current itself, which assists the shunt current 
in exciting the field magnets. In a correctly compounded 
machine the increase of magnetization due to the main 
coils is sufficient, and no more than sufficient, to keep the 
external electro-motive force constant at all currents 
which can safely be passed through the machine. We 
say the machine is accurately compounded for constant 
terminal pressure. 

Now it is easy to see that we can overdo the thing, by 
putting on somewhat finer shunt wire, which will lower 
the electro-motive force when the machine works on open 
circuit or on a circuit of high resistance ; and by in- 
creasing the number of main coils so as to make the ex- 
citing power of the main current preponderate over that 
of the weaker shunt. In this case the increase of internal 



EXPERIMENT WITH SHUNT MOTOR. 163 

electro-motive force will more than counterbalance the 
loss through self-induction and resistance, and the result 
will be that up to a certain limit the external electro- 
motive force will rise as the current increases, Such an 
over-compounded machine could therefore be used as a 
generator, the receiver being an ordinary shunt machine, 
and we would thus obtain a system of transmission of 
energy at constant speed. 

Theoretically this is quite correct, but in practice there 
arises a difficulty due to the fact that the polarity of a 
compound machine can easily be reversed, especially if 
the influence of the main coils is considerably greater 
than that of the shunt coils. The author has attempted 
to establish such a system of transmission of energy at 
constant speed, but failed for the above reason. The 
failure was, however, more instructive than would have 
been the case had the system worked with theoretical per- 
fection, and an account of it was published at the time in 
" The Electrician" (April, 1885), of which the following 
is an abstract : — 

"A series-wound dynamo, when used as a motor, runs 
in the opposite direction to that in which it has to be 
driven when used as generator. To make the machine 
run in the same direction (call it forward), the coupling 
between field and armature must be reversed. With a 
shunt machine this is not so ; the coupling between field 
and armature remains the same when used as a motor, 
and it runs always forward. The shunt machine used by 
the author was driven by a current from an over-com- 
pounded dynamo, the shunt of which was weak as com- 
pared to the main coils, and when the motor was doing 
little or no external work it behaved in a most erratic 
manner, running backward and forward alternately. At 



164 ELECTRIC TRANSMISSION OF ENERGY. 

every reversal excessive sparking took place at the 
brushes of both the motor and generator, and it was 
clear that both machines were overstrained and would 
speedily come to grief if the circuit were not interrupted. 
To explain what takes place under these circumstances 
we will start with the assumption that the generator is 
kept running at a constant speed, and that the motor is 
switched on whenever power is required. This is the 
usual practice where motive power is used at intervals for 
industrial purposes. Since the leads from the generator 
remain always charged, the moment we switch the motor 
on, a large current will pass through its armature and a 
small current through its magnets. As the motor is at 
rest there is no counter-electro-motive force to oppose the 
flow of electricity through the armature, and the result is 
a momentary excess of current. The immediate effect of 
this is to start the armature revolving at a high speed 
before the magnets have had time to become fully excited, 
for it must be remembered that an armature will revolve 
in a non-excited field, though with considerable waste of 
current. The speed required to produce a given counter- 
electro-motive force is the greater, the weaker the excita- 
tion of the field, and hence the motor starts off at a much 
faster speed than it would have in regular work with its 
magnets fully excited. On account of self-induction in 
the shunt field magnet coils, which is considerable, the 
magnets require some time to become fully excited, and 
whilst the strength of the field is growing the armature is 
gathering speed and storing mechanical energy. When 
at last the field magnets are saturated, the armature of 
the motor has attained such a speed that its counter- 
electro-motive force not only equals, but exceeds the dif- 
ference of potential maintained between the leads by the 



EXPERIMENT WITH SHUNT MOTOR. 165 

generating dynamo, and the current is forced back through 
it. For the time being the motor acts as a generator, the 
energy stored mechanically in its revolving armature 
being returned to the circuit in the form of current. This 
reverses the polarity of the compound dynamo (its shunt 
coils being weak, as stated above), and now both the 
generator and the armature of the motor are working in 
series, the generator assisting instead of opposing the 
current started by the motor. At this moment we have 
the following state of things : — The field magnets of the 
motor have just attained their maximum of magnetization 
with their original polarity ; the polarity of the generator 
has been reversed, and an excessive current, in an oppo- 
site direction to that which produced motion, flows 
through the armature of the motor. Consequently the 
latter is quickly brought to rest, and started backward at 
a high speed. It now opposes a certain counter-electro- 
motive force to the current from the generator, but it is 
not an increasing force as before. It is a decreasing one, 
because the original excitation of the motor field magnets 
is gradually vanishing, by reason of the reversal of 
polarity in the main leads, from which these shunt coils 
are fed. Just as it took a certain appreciable time of 
several seconds for the magnets to become excited, so 
does it take time for them to lose their magnetism. 
Eventually there arrives a moment when all the original 
polarity in these magnets has vanished, and when, there- 
fore, the force impelling the armature to run backward 
has also ceased, though there is still an excessive current 
passing through it. A moment later the armature comes 
to rest, and begins to run forward again at a high rate of 
acceleration, when the whole cycle of phenomena just de- 
scribed is repeated, but this time with a current in the 



166 ELECTRIC TRANSMISSION OF ENERGY. 

reverse direction to the first. The third cycle will start 
with a current in the same direction as the first, the 
fourth cycle will start with an opposite current, and 
so on." 

A similar phenomenon was observed by M. Gerard- 
Lescuyer, who used a Gramme series-wound dynamo as 
a generator, and a magneto machine as a receiver. He 
called the phenomenon an electro-dynamic paradox, and 
a description of it will be found in " The Engineer " of 
Sept. 17, 1880. 



CHAPTER VI. 

Classification of Systems according to Source of Electricity — Transmission 
at Constant Pressure — Motors mechanically governed — Self- Regulating 
Motors — Transmission at Constant Current — Difficulty of Self-Regulation 
— Motor for Constant Current made Self-Regulating — Application to 
Transmission over large Areas— Continuous Current Transformator — 
Transmission between two Distant Points — Loss of Current by Leakage — 
Theory — Commercial Efficiency — Conditions for Maximum Commercial 
Efficiency — Self- Regulation for Constant Speed — Practical Example. 

It will be necessary to distinguish between different sys- 
tems of electric transmission of energy, according to the 
source of electricity. An almost endless variety of cases 
may present themselves in different applications of elec- 
trical transmission, but three systems are of special in- 
terest, because most frequently occurring in practice. 
These are the following : — 

1. Transmission of energy from primary or secondary 
batteries at short distances to one motor only. 

2. Transmission of energy from one or several dynamos 
to a number of motors placed upon the same circuit, but 
working independently of each other. 

3. Transmission of energy between two distant points 
by means of one generator and one motor. 

We may also make another classification according as 
the motors are intended for a constant or variable load, 
or a constant or variable speed. Generally speaking, the 
systems of transmission coming under heading 1) are not 
required for a constant load, nor is it of any great impor- 



168 ELECTRIC TRANSMISSION OF ENERGY. 

tance that the speed should remain constant under a 
variable load. We shall not enter into a minute descrip- 
tion of these cases here, as the investigation of electric 
tramways and railways, worked by accumulators, will 
afford ample opportunity of entering into details. 

System 2) is that presenting most difficulties on account 
of the condition that all the motors must be independent 
of each other. The case is further complicated by the 
requirement that each motor should run with the same 
speed when empty or loaded. A moment's consideration 
will show that the last condition is an absolute necessity 
if we would make the electric transmission of energy of 
real practical use to small domestic industries. The 
artisan or small manufacturer would have his motor con- 
nected to a common system of service leads, and when- 
ever he required power he would switch the current on 
to his motor. In doing so he must not disturb any other 
work which; at the same time, may be done elsewhere 
from the same service mains, such, for instance, as light- 
ing or working other motors ; and further, his motor 
should always run at the same safe speed, whether it is 
giving him little or much mechanical energy. Most 
operations requiring the use of tools as turning, planing, 
&c, can only be properly performed at a certain fixed 
rate of speed, and the machinery must be kept going at 
that rate at all times. 

System 3) presents difficulties of a different nature. 
Since we have to deal only with one generator and one 
motor, it is easier to make each fit the other, and as a 
rule the load is fairly constant, so that regularity of speed 
is not difficult to obtain. In this case the difficulty lies 
more in the necessity of proper insulation of line and 
machinery. Generally speaking, the system is required 



SYSTEMS OF ELECTRIC TRANSMISSION. 169 

for long distance transmission, and to obtain an econo- 
mical arrangement, both as regards first cost and com- 
mercial efficiency, the use of a high electro-motive force 
is necessary. This entails some danger to human life, 
and some difficulty in maintaining an efficient insulation. 
Both these points can, however, be satisfactorily dealt 
with, if proper care is used in the design and execution 
of the work. As regards the danger to human life in- 
volved in the use of electric currents of high pressure, 
this is generally greatly overrated. It is quite possible 
for a man who with both hands should touch the positive 
and negative wires in a non-insulated part, to be killed or 
severely injured if the pressure is over two or three thou- 
sand volts, but the accident can be rendered almost im- 
possible if due precaution is taken. A circular saw if 
only lightly touched whilst revolving will cut a man's 
finger oiF, and what can be more dangerous than a pair 
of powerful spur wheels ? Yet we have found means of 
protecting life very effectually from destruction by purely 
mechanical means, and the experience of the past few 
years has shown that equally efficient protection can be 
provided from the electrical danger. 

System 2) is best described as electric transmission 
and distribution of energy from one central station to 
several distant points. This distribution can be made on 
the parallel or on the series system. In the first case the 
electro-motive force (or pressure) between the positive 
and negative mains must be kept constant, and the motors 
are connected all in parallel from the mains ; in the second 
case the current passing through the mains must be kept 
constant, and each motor, when at work, is traversed by 
the same current. The pressure at the station must be 
the greater the greater the number of motors at work. 



170 ELECTRIC TRANSMISSION OF ENERGY. 

In the first case the pressure is kept constant, but the 
current delivered into the mains must be the greater the 
greater the number of motors at work. We have thus to 
distinguish between distribution at constant pressure and 
distribution at constant current. 



Electric Distribution of Energy at Constant Pressure. 

We must now inquire into the theoretical conditions of 
this case. It will be evident at the outset that for econo- 
mical reasons any attempt to obtain constancy of speed 
by the use of artificial resistances can only lead to a 
partial and not very satisfactory solution of the problem, 
and had better not be made if other means are at hand. 
This happily is the case in the present instance. We 
have two means by which we can without waste regulate 
the power of the motor to the work and yet keep it 
running at a constant speed. First we may apply a 
mechanical device by which the current is periodically 
cut off in proportion as the work is cut off, and, secondly, 
we may apply an electric device in the shape of special 
winding of the field magnets of the motor by which the 
torque exerted by the armature is automatically regulated 
so as to correspond to the mechanical load. As regards 
the first system, Professors Ayrton and Perry have in a 
paper on Electro-Motors and their Government 1 shown 
how this can be done. They say : "The method of cutting 
off the power as hitherto employed has this serious defect, 
that instead of the power cut off being directly in propor- 
tion to the work cut off, the arrangements have been such 

1 " Journal of the Society of Telegraph Engineers and Electricians," No. 
49, vol. xii. 1883. 



PERIODIC GOVERNORS. 171 

that either all power was cut off or none, so that the 
motion of the motor was spasmodic, just as in an ordinary- 
gas-engine, which suffers from the same defects, that full 
charge of gas or no charge are the usual only alternatives. 
An electro-motor governor of this type, which may be 
called a ' spasmodic governor,' consists merely of a ro- 
tating mercury cup into which dips a wire, which makes in 
this case contact with the mercury, and so completes the 
circuit when the speed is slow, but which, on account of 
the hyperbolic form assumed by the service of the mer- 
cury as the speed rises, ceases to dip into the mercury at 
high speed, and so breaks contact." Later on the in- 
ventors say: " The first improvement we made in govern- 
ing consisted in replacing the ' spasmodic governor ' by a 
' periodic governor/ With our periodic governor the 
power is never cut off entirely for any length of time, 
but in every revolution power is supplied during a portion 
of the revolution, the proportion of the time in every re- 
volution during which much power is supplied to the time 
during which less is supplied depending on the amount of 
work the motor is doing. Our periodic governor, then, 
differs from the spasmodic governor in the same way that 
a good loaded steam-engine governor differs from the 
ordinary governor of a gas-engine. One of the ways of 
effecting this result is as follows : a brush, A, Fig. 67, 
lies on the rotating piece, B K, the cylindric surface of 
which is formed of two conducting portions connected 
with one another through any resistance, and the brush, 
A, is moved along the cylinder B K under the action of 
the governor balls. When the brush A is touching the 
contact part i?, the motor is receiving current directly, 
but when it rests on the part K, the motor receives cur- 
rent through the resistance which is interposed between 



172 



ELECTRIC TRANSMISSION OF ENERGY. 



B and K. If the governor balls fly out, the brush is 
moved along, i?, K, so that there is contact with K during 
a greater part of the revolution than before ; and if the 
governor balls come together, the speed of the motor being 
too small, the brush is moved in tin opposite direction so 
that it makes contact with B for a longer time during each 
revolution. If the motors are in series, we arrange that 
the periodic governor shunts the current periodically, in- 
stead of introducing resistance. In this case the connec- 
tions are as follows : B is made of wood, while K is made 

Fig. 67. 




PERIODIC GOVERNOR. 



of metal. iTis connected to one end of a shunt coil, the 
other end of the shunt being connected to one of the ter- 
minals of the motor and A is connected to the other ter- 
minal of the motor. If, then, A rests on B, the shunt is 
inoperative and all the current passes through the motor ; 
whereas, if it rests on K^ the shunt is in operation, and 
part of the current only passes through the motor." It 
will be seen that both these governors invented by Pro- 
fessors Ayrton and Perry, have partially, at least, the 
fault of depending on artificial resistances whether they 



SELF-REGULATING MOTOR. 173 

be used for parallel or series work. The loss of energy 
thus occasioned can be reduced by making the resistance 
high for parallel, and low for series work, and on purely 
theoretical grounds it could even be entirely prevented 
by making the resistance infinite, that is, breaking the 
circuit altogether during a portion of each revolution 
when working in parallel. But this would produce an 
unequal turning force, and would also entail destructive 
sparking between the brush, A, and the contact pieces 
B and K. Even if the resistance between B and iTor 
that of the shunt coil between iTand one terminal of the 
motor is fairly low, there must be some sparking ; and 
the inventors say in their paper that with any such 
governors it is difficult to entirely prevent sparking, and 
that on this account motors wound so as to be self- 
regulating without any mechanical device are preferable. 

Broadly speaking, the self-regulating motor is the con- 
verse of the self-regulating dynamo wound for constant 
pressure. In a properly compounded dynamo the pres- 
sure at the terminals must remain constant, although the 
resistance of the external circuit may vary between wide 
limits, causing an inversely proportional variation in the 
external current. The power required is approximately 
proportional to the current. The machine works, there- 
fore, under these conditions : Speed constant — Electro- 
motive force constant — Current variable — Power re- 
quired to drive the machine also variable, but proportional 
to current. Now, in a self-regulating motor the conditions 
are : Electro-motive force constant — Speed constant — 
Power variable — Current required to drive the motor 
also variable, but proportional to power. 

It has already been pointed out that in a general way 
dynamo and electro-motor are convertible terms ; and 



174 ELECTRIC TRANSMISSION OF ENERGY. 

although there are cases when it is impracticable to work 
a motor as a dynamo, it is always perfectly easy to work 
a dynamo as a motor. From this general convertibility 
it is reasonable to expect that a properly compounded 
dynamo can without any alteration in the connection be- 
tween its field magnet coils and armature, be used as a 
self-regulating motor, the only condition being that it shall 
be supplied with current at a constant electro-motive 
force. When speaking of a self-regulating motor in the 
sense that its speed of rotation shall automatically be 
kept constant whatever variation might occur in the load 
or mechanical resistance which the armature of the motor 
has to overcome, it must be understood that this refers 
only to such cases where the load varies between zero 
and a maximum not beyond the capability of the motor. 
If we throw an excess of load on to the motor, it will pull 
up or slacken speed, and thus cease to be self-regulating, 
just as the electro-motive force at the terminals of the 
best compound- wound dynamo will be lowered if we 
allow an excess of current to flow. But within a reason- 
able limit of load in the case of the motor, and a reason- 
able limit of current in the case of the dynamo, both 
machines can be made self-regulating, and this result is 
obtained by the same means, that is to say, the same 
winding which will make the dynamo give a constant 
electro-motive force, will make the motor run at a con- 
stant speed. This result might be expected on the 
ground of the general convertibility of these machines, 
but since it is of great practical importance, special proof 
is desirable. This can be easily obtained from our formulas 
in Chapter III. According to equation 7) the torque 
exerted by an armature current, C a , in a field of Z lines, 
is in absolute measure : 



SELF-REGULATING MOTOR. 175 

T = ZNtC. 

It is independent of the speed, and since Nt is constant 
for any given motor, the torque or turning moment 
exerted by the armature is directly proportional to the 
product of the strength of field and armature current. 
By increasing either or both these factors we are able to 
overcome our increased load. Since the electro-motive 
force is supposed to be constant, it is evident that a varia- 
tion in load must be compensated mainly by a variation 
in current. Assuming that the ends of the shunt coils 
are coupled to the terminals of the motor — not to the 
brushes — we have, retaining the notation of Chapter III., 
the following equations : 

E 

Cs= — C a =C m . 

7* 

E 6 = E t - r m C m E a = E t - (r m + r a ) C a . 
The counter- electro-motive force E a is, according to 
equation 5) expressed in volts by 

E a = ZNtnlO* 5) 

E t ~(r m + r a ) C a = ZNt?ilO-\ 
Now the condition under which the motor is to be used is 
that the electro-motive force at its terminals E t9 shall be 
kept constant. We have, therefore, 

Constant E t = (r m + r a ) C a + Z Nt n 10~ 6 . 
Since the speed n must also remain constant if the motor 
is to be self-regulating at all loads, the only variables are 
C a and Z, which have to satisfy the above equation. In 
other words, we may regard the field Z as a function of 
the armature current C a , and the condition that the 
motor be self- regulating is brought down to this, that 
the strength of its field shall depend on, and vary in a 



176 ELECTRIC TRANSMISSION OF ENERGY. 

certain manner with the current passing through the 
motor. 

Z= ^-{r+r a ) C a 10 _ 6 

Ntn 
We see by this equation that Z will be the smaller the 
greater C a , and since C a is almost directly proportional 
to the mechanical load of the motor, we arrive at this, at 
first sight, startling result : that the heavier the work we 
impose upon the motor, the weaker must be its field. It 
might have been thought that as additional load is thrown 
on, we ought so to arrange matters that the magnetism 
of the field magnets becomes strengthened, and able to 
exert an increased magnetic pull on the armature. But 
a moment's reflection will show that the effect of such an 
arrangement would be to reduce the speed. The mag- 
netic pull exerted by the field magnets upon the armature 
does not depend on the strength of magnetism in the field 
magnets only, but is the product of that quantity and the 
current in the armature coils. An increase of pull may 
therefore be brought about either by making the field 
stronger, or by increasing the current in the armature, or 
by both means combined. If we make the field stronger, 
we not only increase the magnetic pull exerted on the 
armature, but we also increase the counter-electro-motive 
force, as will be seen from equation 5), page 82, and thus 
check, or at least reduce, the flow of current through the 
armature at the very moment when we want most power. 
The motor would thus run slower until its reduced 
counter-electro-motive force again allows a current to pass 
of sufficient strength for the work imposed on the motor. 
If, on the other hand, we seek the increase of power by 
allowing more current to pass through the armature, we 
do not increase the counter-electro-motive force, but we 



COMPOUND DYNAMO USED AS MOTOR. 177 

have a slight increase in the loss of electro-motive force 
due to the resistance of the armature. To compensate 
for this slight increase of loss, it is necessary to weaken 
the field somewhat for heavy currents, and thus bring 
about the reduction of counter-electro-motive force by an 
amount corresponding to the increased loss of electro- 
motive force due to the resistance of the armature. If 
the motor runs without doing external work C a is almost 
zero, and we have the strongest field, 

E t 10 6 



Z. 



Ntn> 



which is entirely due to the shunt coils. Let now a load 
be thrown on. The immediate effect will be to slightly 
reduce the speed. The counter-electro-motive force which 
previously was nearly equal to E„ will thereby become 
somewhat reduced, thus allowing a considerable current 
to pass through the armature and the series coils of the 
magnets. This again accelerates the armature until the 
normal speed is reached. The direction of winding of 
the series coils must be evidently such that the main 
working current tends to demagnetize the field magnets. 
Now in an ordinary compound-wound dynamo, the series 
coils are wound and connected in such a way that the 
main current tends to increase the magnetism produced by 
the shunt coils. If we use such a dynamo as a motor, 
the current in the shunt coils will remain the same as 
before, the current in the armature will flow in the re- 
verse direction, and therefore produce motion — instead of 
resisting it, as is the case when the machine is worked as 
a dynamo ; and the current through the series coils will 
also flow in the reverse direction, thus tending to weaken 
the field magnets. It will be seen that these are precisely 

ST 



178 ELECTRIC TRANSMISSION OF ENERGY, 

the conditions which our theory indicates as necessary, in 
order to make the motor self -regulating, and we find that 
it is correct to say that a compound-wound machine can 
be used either as a self-regulating dynamo or as a self- 
reguLiting motor. There may be slight differences in 
the exact proportion between shunt and series coils in 
both cases, but the general principle of compounding is 
the same for either purpose. 

A question of considerable practical importance is that 
of the relation between the weight of the motor and the 
maximum of mechanical energy it can give out. Since 
that maximum must be given out when the field is 
weakest, whereas in a non-self-regulating motor the 
arrangements can always be so made that the maximum 
is given out when the field is strongest, it is evident that, 
for a given power, the self-regulating motor must be 
heavier. This is certainly a drawback, and it becomes 
necessary to know what price, in the shape of increased 
weight, we have to pay for the advantage of automatic 
regulation. Our formula for Z enables us to form a 
rough estimate of this increase in weight. The difference 
between the initial value of Z and the minimum value 
is due to the product (r m + r a ) C a . The greater this 
product, the more must the field be weakened, and the 
smaller is the maximum of power obtainable with a given 
weight of motor. It is therefore of importance to keep 
the product (r m + r a ) C a as small as possible, and 
since C a , which we must consider as the primary source 
of power, cannot be reduced, it is evident that the re- 
sistance of series coils and armature should be as small 
as possible. Now, in a good modern motor, the loss of 
electro-motive force occasioned by the resistance of these 
parts, varies between 5 and 10 per cent, of the electro- 



DISTRIBUTION AT CONSTANT CURRENT. 179 

motive force applied at the terminals ; take 7 per 
cent, as a fair average, and we find that if the initial 
field is represented by, say, 1,000 lines, the field at full 
work will contain 930 lines. Now if the motor were not 
self-regulating, the field at full power would contain 
1,000 lines, and thus be able to develop about 7^ per 
cent, more mechanical energy. If, on the other hand, 
we wish the two motors to develop the same maximum 
of mechanical energy, the field magnets of the self-regu- 
lating motor would require to have 7^ per cent, more 
cross sectional area. Since series and shunt coils act 
differentially, a larger amount of copper is also required. 
This excess would probably amount to about 2^ per cent, 
of the total weight, so that in all the self-regulating motor 
will weigh 10 per cent, more than an ordinary motor which 
is not self-regulating. This does not seem too high a 
price to pay for the safety and general comfort of a self- 
regulating motor, and the experience gained in American 
and Continental towns having central electric light 
stations from which current is supplied to a network of 
mains on the parallel system has proved that it is perfectly 
practicable to utilize the same mains for distributing mo- 
tive power to artisans and small manufacturers by supply- 
ing them with such self-regulating motors. 

Electric Distribution of Energy at Constant Current. 

This problem is not of so easy solution as the distribu- 
tion of energy at constant pressure, and the difficulty is 
a fundamental one. It lies in this, that there is no direct 
connection between the speed of a motor and the current 
which flows through its armature. There is a direct con- 
nection between speed and electro-motive force, and, 



180 ELECTRIC TRANSMISSION OF ENERGY. 

therefore, self-regulation is possible without the use of 
any external appliance in the shape of a mechanical 
governor or other apparatus which controls the power. 
But where the current is constant, some kind of external 
governor is necessary. This follows also immediately 
from M, Marcel-Deprez's experiments cited in Chapter 
III., page 103. We have seen that the speed was 
totally independent of the current, the latter remaining 
throughout the range of each experiment practically con- 
stant, whereas the speed was in some cases increased five- 
fold, by simply increasing the electro-motive force of the 
source. When a number of motors are coupled in series, 
as would be the case in a general system of distribution, 
the difficulties are much increased. To test this matter 
experimentally the author has placed three precisely 
similar motors (series-wound) in series into the same 
circuit. The current was supplied by a dynamo, and 
the three motors were loaded by brakes to as near as 
may be the same amount. It was then found quite im- 
possible to keep all three motors going for any length of 
time at the same speed. The least irregularity in the 
current, or the least variation in the friction of the brakes, 
would cause first one and then the other motor to come 
to rest, whilst the speed of the remaining motor increased 
to a dangerous extent. 

Professors Ayrton and Perry have in the paper above 
mentioned proposed to make motors self-regulating if 
worked by a constant current in the following way : 
The field magnets, Fig. 68, are wound differentially with 
a fine wire coil, which is a shunt to the armature only, 
and a thick wire coil which is in series with the armature 
and main current. The armature and shunt coil consti- 
tute a shunt motor, the armature and main coil a brake 



SELF-REGULATING CONSTANT CURRENT MOTOR. 181 

generator which is intended to absorb any surplus power 
if the load is thrown off. As far as the author is aware 
the system has not been tried in actual practice, and 
there are theoretical reasons for expecting that it would 
not work. Prom equation 7) it will be evident that the 
field must be strongest when the load is greatest. Now 
suppose that the differential winding could be so propor- 
tioned that for a given load the field is exactly of the 
right strength to produce the normal speed. Now let a 
very slight additional load be thrown on. The immediate 



Fig. 68. 




effect will be to slightly reduce the speed, and in conse- 
quence of the reduction in speed the magnetizing current 
in the fine wire coil will also be reduced. The field will 
thus be slightly weakened. This will further reduce the 
speed and again weaken the field, and so on, until the 
armature comes to rest. At that moment the magnetizing 
influence of the main coils, which is in the opposite direc- 
tion to that of the shunt coils, will alone exist, and the 
field magnet instead of presenting a N pole to the arma- 
ture, as shown in the illustration, will present a S pole 
to it. The tendency must therefore be to reverse the 



182 ELECTRIC TRANSMISSION OF ENERGY. 

motion, and thus the slight addition of load has not only 
brought the armature to rest, but actually caused a 
tendency to run backwards. Whether it will run back- 
wards depends on the relative magnetizing power of the 
main and shunt coils. 

In a subsequent paper read by the same authors before 
the Physical Society on May 26, 1888, they suggest 
to make motors self-regulating for constant current by 
omitting the series coils on the field magnets altogether, 
and inserting into the armature circuit a storage battery, 
the electro-motive force of which helps the current on. As 
far as the author knows no practical test of this system 
has been made, and it is easy to see that the objection of in- 
stability, which was pointed out above for the first arrange- 
ment, also applies in this case. Constant current motors are 
extensively used in the United States on arc light circuits, 
but in all cases the regulation of speed is effected by some 
additional mechanism which either shifts the brushes or 
alters the exciting power. The attempt to make a con- 
stant current motor self -regulating without such additional 
devices has very little chance of practical success. 

An arrangement devised by the author, and which 
seems to promise somewhat better to fulfil the condition 
of constant speed, is shown in Fig. 69. A is the armature 
of a series-wound motor mounted upon a spindle, to 
which is also attached the armature a, of a small series- 
wound dynamo which has no other work to do but to 
supply current for demagnetizing the field magnets of 
the motor. The main current magnetizes them in the 
direction, say, from B to (7, the auxiliary current from 
the dynamo acts in the direction f to g, and tends to de- 
magnetize them, b c is the field magnet coil of the 
dynamo. Now for each dynamo working on a closed 



SELF-REGULATING CONSTANT CURRENT MOTOR. 183 

circuit of constant resistance, as in the present case, there 
exists a critical speed at which it will begin to give a 
current of some strength. Below that speed it gives 
hardly any current, and above that speed it gives almost 
at once the full current. The motor should be so geared 
as to run at the critical speed of the little auxiliary 
dynamo. If now an additional load be thrown on, the 
immediate result will be to reduce the speed of the motor, 
thereby causing the armature of the dynamo to run 

Fig. 69. 



[WW1 




UW\AAJ/ 



^Y/WWl 




below its critical speed. The dynamo will thus partly or 
entirely lose its current and the demagnetizing influence 
which previously has kept the field below its full strength, 
will to a greater or lesser degree be withdrawn. The 
strength of the field will thus be increased, and an 
additional magnetic pull will be brought to act on the 
armature, by which it can overcome the increased load. 
In case the load be entirely thrown off*, the motor will 
have a tendency to race, but this tendency will be im- 
mediately checked by the auxiliary dynamo, the current 



184 ELECTRIC TRANSMISSION OF ENERGY. 

from which increases considerably with a very slight 
increase of speed. Its demagnetizing influence is thus 
enormously increased, and the field of the motor is 
weakened to such an extent that there is just power 
enough left to drive the dynamo but no more. To make 
this arrangement successful it is necessary that the field 
magnets of the auxiliary dynamo be made of very soft 
iron, so as not to retain any considerable amount of per- 
manent magnetism, which would alter the critical point 
as between an increasing and decreasing speed. The 
more sensitive and unstable the dynamo can be made, 
the better. For this reason it is also necessary to place 
the two armatures a considerable distance apart on the 
same spindle, so that the field magnets of the motor may 
not induce magnetism in the field magnets of the dynamo, 
and thus disturb the critical point. In practice it would 
probably be found necessary to place a bearing between 
the two armatures, and that could easily be so shaped as 
to act as a screen between motor and dynamo. 

According to the classification made in the beginning 
of this chapter we have now to consider 

System 3), which comprises the transmission of energy 
between two distant points by means of one generator and 
one motor. 

Let E a , E 6 , and E„ represent respectively the electro- 
motive force in the armature, at the brushes and at the 
terminals of the generator, and let e a , e 6 , and e t , repre- 
sent the same for the motor. Let B a , R m , represent the 
resistance of the armature, and magnetizing coils of the 
generator, and r a , r m , represent the same for the motor, 
then we have, according to the equations 15) to 22), 
if both machines are series-wound, the following rela- 
tions : 



LOSS OF CURRENT BY LEAKAGE. 185 

Generator. Motor. 

E a = E b + CR a . e a = e b - cr a . 

E b = E t + CR m . e b = e t - cr m . 

E t = E a - C(R a + R m ). e t = e a + c(r a + r m ). 

C being the current sent by the generator into the line, 
and c being the current received by the motor. If the 
insulation of the line were perfect, these two currents 
would be equal ; but in practice some small leak of cur- 
rent from the positive to the negative circuit, w T hen the 
line extends over several miles, might take place and 
then we must assume 

C>c. 

The loss of current C — c represents, as far as the 
generator is concerned, a waste of energy expressed by 
the product 

E t (C — c) watts. 

As far as the motor is concerned, this leak not only re- 
duces the current which is available at the receiving 
station, but it has also the effect of reducing the available 
electro-motive force e t beyond the value corresponding to 
the current c. It will be clear that unless the leak occurs 
close to the generator, part of the line will have to carry 
a current larger than c, and thus the loss of electro-motive 
force due to the resistance of the line must be greater 
than the product of that resistance and the motor-current 
c. If the line is throughout its entire length equally well 
insulated, each unit of its length will have the same in- 
sulation resistance, which should be very high in com- 
parison to the conducting resistance itself. In a perfect 
line it should be infinite, but, as remarked above, this 
may not be obtainable in an overhead circuit going many 
miles across country. Let g represent the conducting re- 



186 ELECTRIC TRANSMISSION OF ENERGY. 

sistance of the line, and let i denote the insulation resis- 
tance between the positive and negative lead for unit 
length. If the distance from the generator to the 
motor be I, the total insulation resistance as measured on 

a Wheatstone bridge would be ~j. Knowing this from 

actual measurement, it might be thought that by the 
application of Ohm's law we could easily find the leak, 
C — c, by simply dividing the electro-motive force be- 
tween the wires by the insulation resistance. This would, 
however, not be correct, for the simple reason, that the 
electro-motive force between the wires is not a constant, 
but diminishes in a certain ratio as we approach the dis- 
tant end of the line, the actual law by which this diminu- 
tion takes place depending not only on the resistance of 
the line and the current, but also on the insulation resis- 
tance itself. The question is therefore not so simple as it 
at first sight appears. An approximate solution suffi- 
ciently accurate for practical purposes is the following : 
Let 6 represent the electro-motive force between the 
leads at the distance x from the generator ; let the dis- 
tance be increased to x + dx and the leak of current cor- 
responding to length dx be dc, the drop in electro-motive 
force corresponding to that length being de. Then the 
following equations evidently obtain : 

— d s = c -j dx. 

— dc = — dx. 
i 

From these equations we obtain 

£ d e = -ji c dc, 



LOSS OF CURRENT BY LEAKAGE. 187 

and by integration 

£ 2 — — c 2 = Constant. 

To find the constant we apply the formula to the home 
end of the line where e = E n c = C 9 and obtain between 
that and the far end the relation 

J?, , -«, , =v|i , (C w -e>), 

from which we find 



c = </ C 2 - L{Et-^\ 

$ l 

This gives the current arriving at the motor, but in a 
somewhat inconvenient form. To simplify the expression 
we develop the square root into a series, and since the 
second term is very small in comparison to the first we 
can neglect the second and subsequent powers. 

1 l( E t >-e> ) 

Now E; - e, 2 = {E t + e t ) (E, - e t ) and ~ = J, the 

total insulation resistance of the line. Hence 

/ E, + e, \ 1 E,-e 
c _ C {—2~J j. -Jc— 

The leak of current is 

c ■- - '-(H*)* *tP 30) - 

E + e 

Now — *— — ■ is the average electro-motive force between 

the out and home lead ; and ( — *— — - j -= represents the 
current which under that average electro-motive force 



188 ELECTRIC TRANSMISSION OF ENERGY. 

would flow through J y the total insulation resistance. This 

E, e 

current, multiplied by ' , gives the actual leak. It 

will be observed that $ (7, being the product of a resistance 
and a current, represents a difference of potential, and in 
this case it represents the electro-motive force which would 
in a line of perfect insulation be required to drive the 
full initial current C through the circuit, supposing the 
far ends were in metallic contact, g C represents, there- 
fore, the loss of electro-motive force if there were no leak. 
The actual loss, JE t — e t9 is naturally somewhat greater, 
and thus the quotient between the two must always be 
greater than unity. From this it follows that the loss of 
current due to leakage along the line is slightly greater 
than the figure we obtain by dividing the average electro- 
motive force by the total insulation resistance. Where 
the insulation resistance is very high, and the conduct- 
ing resistance very low, the leak will with sufficient 
accuracy be expressed by 



( Et + e % \ 1 



but when the conditions are less favourable formula 30) 
should be used. 

It is necessary in this place to briefly consider the in- 
fluence of the leak on the total efficiency of a system of 
electric transmission, especially with reference to the most 
economical speed of the motor. In text books, and in 
scientific articles on the subject, the assumption is gene- 
rally made that the insulation of the line is perfect. This 
may be so in some favourable cases, but a general theory 
must include all cases ; it should, therefore, take the leak 
into account. As far as the writer knows, this has only 
been done by Professor Oliver Lodge in his treatise on 



LEAKAGE AND ECONOMICAL SPEED. 189 

the transmission of power by dynamo-machines, published 
in " The Engineer," 1883. It is also generally stated 
that the efficiency is the greater, the nearer the counter- 
electro-motive force of the motor approaches the electro- 
motive force of the generator. It has already been 
pointed out that this is quite wrong (see Chapter V., 
page 154), even if the motor be worked by a current of 
constant electro-motive force, such as would be the case 
if the generator were a self-regulating dynamo placed 
closed to the motor, and connected with it by leads of 
practically no resistance and perfect insulation. But 
when the leads have considerable resistance, and especially 
if their insulation is not absolutely perfect, the statement 
above referred to and which is carefully perpetuated by 
successive writers, becomes still more erroneous. From 
equation 30) it will be seen that the leak is the greater, 
the greater e t . At the same time an increase of e t has 
the effect of checking, or at least diminishing, the working 
current c, thus reducing the amount of energy received. 
Since the energy lost by leakage increases with the 
counter-electro- motive force, whilst the energy actually 
given out by the motor at first increases with the counter- 
electro-motive force up to a certain point, but beyond it 
decreases again, it will be clear that high efficiency can- 
not be obtained by allowing the counter-electro-motive 
force to approach too near to the electro-motive force of 
the generator. In the following investigation we shall 
assume for the sake of simplicity that there is absolutely 
no leak in the line. The results obtained will, therefore, 
be to some extent inaccurate, but they can be rectified 
by using equation 30). Thus with a perfect line we 
would obtain certain values for C = c and E t ; and the 
generator would have to give the current and electro- 



190 ELECTRIC TRANSMISSION OF ENERGY. 

motive force thus determined. Now assume that, after a 
certain time, the line begins to leak. This will reduce 
the energy received by the motor, and consequently also 
that given out by it. It is evident that this loss can be 
compensated by running the generator at a higher speed ; 
in other words, by increasing ~E t and C beyond their 
original values. A similar plan we follow in the mathe- 
matical investigation. We assume at first that the insu- 
lation of the line is perfect, and we are thus enabled to 
use formulas of great simplicity. This gives a certain 
set of conditions for the generator. If the line is in 
reality in as perfect a state as assumed, the problem is 
solved. If, however, the line leaks, we rectify the 
values for E t and C by using equation 30). This gives 
a new set of conditions for the generator, and the 
mechanical energy necessary for actuating the generator 
must be calculated for these new conditions. The condi- 
tions of the motor are not altered thereby. 

The electro-motive force lost in the line is $c 9 which 
must be equal to the difference of electro-motive forces at 
the terminals of generator and motor 

E t = $c -f e t . 

The internal electrical energy of the generator is c E a9 
that of the motor is c e a , and the proportion between the 
two is the electrical efficiency of the whole system. 

6 

Electrical efficiency = -=^-. 

By combining this expression with the above equations 

we find also : Electrical efficiency 

p 
= z± 31) 

«.+ e($ + r, + r.+S J +i2.) ;- 

It is evident that whatever may be the resistance of the 



ELECTRICAL EFFICIENCY. 191 

line s, or in other words whatever may be the distance 
to which the energy has to be transmitted, we can always 
obtain the same electrical efficiency by suitably vary- 
ing c and e a . The higher e a9 the counter-electro-motive 
force of the motor, the greater is the electrical efficiency. 
Now there are two means by which we can raise the 
counter-electro-motive force. The one is by increasing 
the speed, the other by employing machines containing a 
large number of turns of wire (Ni) on their armatures. 
The first expedient is limited by the mechanical diffi- 
culties generally attendant on the use of excessive speeds, 
and the latter by the difficulty that the internal resistance 
of the machines is the greater the more turns of wire they 
contain. This, in itself, would not effect the result if the 
electro-motive force would increase in the same propor- 
tion as the resistance of the machine. But this is not the 
case. If a given size armature core be wound with many 
turns of fine wire, and a precisely similar core with such 
a number of turns of stouter wire, that both windings fill 
exactly the same space, the weight of copper contained in 
the armature wound with stout wire must always be some- 
what greater than in the other, because the space wasted 
by the insulating covering on the wire is less. It is 
clearly not admissible to reduce the thickness of insulation 
in the same ratio as the gauge of the wire. A minimum 
thickness is absolutely necessary for the safe handling 
during the process of manufacture, and moreover the finer 
wire is intended for an armature of higher electro-motive 
force and should for this reason alone have rather better in- 
sulation than the thick wire, which is intended for a lower 
electro-motive force. A good practical rule is to employ a 
covering of cotton about 8 mils for wires of all sizes up 
to about 120 mils. The diameter of the covered wire is 



192 ELECTRIC TRANSMISSION OF ENERGY. 

thus by 16 mils greater than that of the single wire. 
Now it can be shown that the energy wasted in heating 
the wire of the armature is inversely proportional to the 
weight of copper employed, and therefore, with the arma- 
ture of stouter wire, the same electrical output can be 
obtained at a smaller cost of energy wasted in heating 
the wire. The same holds good for the field magnet coils. 
The dynamo wound with stouter wire, will, therefore, be 
the most economical of the two, as its internal resistance 
will be relatively small as compared to its electro-motive 
force. Inversely, if we wind the machines (generator and 
motor) with very fine wire in order to obtain a high 
electro-motive force, we increase their resistances, r a5 r m9 
j? a , i? m , in a somewhat quicker ratio, and thus lower their 
efficiency, taken apart from the line. As regards the 
line resistance j, the higher the electro-motive force the 
better, and it will be evident that taking these two things 
into consideration there must be one particular value for 
the electro-motive force for which the electrical efficiency 
becomes a maximum. This value can be found in each 
given case by assuming different windings for generator 
and motor, and calculating their electro-motive forces and 
resistances. . By inserting the data thus obtained succes- 
sively into equation 31) it can easily be seen which is the 
best. We suppose that the resistance of the line is given. 
The electrical data thus obtained can only be regarded 
as a first approximation to a solution of the problem, be- 
cause they were obtained on the basis of the highest elec- 
trical efficiency, whereas the question of importance is 
the actual or commercial efficiency. It is sometimes as- 
sumed that the commercial efficiency of dynamos and 
motors bears a fixed proportion to their electrical effi- 
ciency, and if that were so we could obtain the actual 



COMMERCIAL EFFICIENCY. 193 

efficiency of our system of transmission by multiplying 
equation 31) with that fixed proportion. But this would 
not be correct. It is evident that the commercial effi- 
ciency of a motor cannot be a fixed quantity, but must 
depend on the power given out, being, generally speak- 
ing, the higher the nearer the work done by the motor 
approaches to the maximum for which it is designed. 
This relation is best expressed in the manner adopted in 
Chapter V., by assuming that a certain minimum of cur- 
rent, y, is necessary to overcome the mechanical and mag- 
netic friction of the motor, and that all the power corre- 
sponding to the difference between this minimum and the 
actual working current is available for external work. 
Similarly we assume that a certain minimum of current, g, 
multiplied by the internal electro-motive force of the 
generator, represents the mechanical energy absorbed by 
mechanical and magnetic friction. We have, therefore, 
the following relations : 

Generator. 
Work absorbed, W— (c+g) E a . 

Motor. 
Work given out, w = (c— y) e a . 
Put R a + R, = R, and r„, + r m = r, then for series- 
wound generator and motor we have 

JE a = e a +c( g + B+r), 

And the commercial efficiency of the whole system is 

y\ = /c — 



\c+gj E a 
( c ~ y \ f. 32) 

\c+g)e m + c{f + R + r) ' 



o 



194 ELECTRIC TRANSMISSION OF ENERGY. 

A question of practical importance is that concerning 
the working conditions under which, in a given system of 
transmission, the commercial efficiency becomes a maxi- 
mum. As already shown, the first condition for attaining 
this object is to work the generator at as high a speed as 
mechanically safe. We shall therefore assume that its 
electro-motive force E a is a constant and as high as pos- 
sible. The variables are the current c, and the counter- 
electro-motive force e a of the motor. If we allow the 
motor to run too slowly it will allow a large current to 
pass, but this will entail a considerable waste of energy 
in heating the line and the two machines. If we speed 
the motor too high, this waste will be very small, but the 
high counter-electro-motive force will only allow very 
little current to pass, and in this case the work done by 
the motor will be small, thus again lowering the commer- 
cial efficiency. Between these two extreme cases there 
must evidently exist one current and one counter-electro- 
motive force for which the commercial efficiency becomes 
a maximum. To find these values we form the first dif- 
ferential quotient, and equate it to zero. Thus the most 
favourable current will be found by the equation 

dc 
and the most favourable counter-electro-motive force will 

be found by the equation - — = o. 

Writing for the sake of brevity E for E a , and e for e a , 
and R for the sum of the resistances $ + R + r 9 the 
first equation gives, 

(c + g) (E - 2 R c + y R) - c (E + y R) + 
Rc 2 + yE=o, 



COMMERCIAL EFFICIENCY. 195 

c being the only unknown quantity. Resolving the 
equation we find 

/ E 

c = —g + y g 2 + £ (g + y) + y g • ■■ • • • 33). 

It will be seen that the quadratic equation has two roots 
or values for c, the one being positive the other negative. 
The latter implies that the current travels in the opposite 
direction, in which case the motor would become the 
generator and vice versa. This does not concern us here, 
as it applies to cases where the receiving machine is 
larger than the generating dynamo, an arrangement 
which no practical engineer would employ. We have, 
therefore, only to deal with the positive root, viz., 

/ E 

c = - g + V g 2 + ft(g + y) + y g 34). 

Having thus determined c, we find the counter-electro- 
motive force of the motor, 

e = E- Re 35). 

To obtain a maximum of commercial efficiency the motor 
must be so speeded that its counter-electro-motive force 
attains the value E — Re. 

dr\ 
By using the equation — = 0, we can also obtain di- 

u e 

rectly the most favourable counter-electro-motive force. 
The solution gives again two values for e, one smaller 
than E, the other larger than E. The latter corresponds 
to the case when motor and generator have changed 
places and need not be further considered for reasons 
above stated. The former value for e is alone of impor- 
tance ; it is given by the formula, 



e = E + Rg - J {E + Rg) 2 - (E + Rg) E - Ry). 36). 



196 ELECTRIC TRANSMISSION OF ENERGY. 

This equation does not clearly show that e must in all 
cases be smaller than E 3 but on developing the expres- 
sion under the square root on the right, we also obtain, 

e = E + Rg - </ R 2 g 2 + R 2 g y + E R {g + y) . 37). 

The same expression is obtained by inserting, 

E-e 

c = -rT 

into formula 34). 

It is evident that the square root in 37) must under 
all circumstances be numerically greater than R g> and 
therefore e must under all circumstances be smaller than 
E. Now, according to the orthodox theory found in text 
books, maximum efficiency is obtained for E = e. This 
could only be if g = o and 7 = 0; that is to say, if the 
dynamo would absorb no energy whatever when working 
an open circuit and if the motor could be kept running 
idle without the expenditure of electrical energy. Both 
these conditions are evidently absurd. 

Since the formulas 32) to 37) have a somewhat com- 
plicated appearance, it might be as well to elucidate their 
application by a practical example. We will assume that 
in a given system of transmission the generator can be 
worked at the safe limit of 1,000 volts and 20 amperes, 
and under these conditions has a commercial efficiency of 
80°/ o « Its internal resistance is 5 ohms. Its external 
electro-motive force at maximum output would there- 
fore be 

1,000 - 20 x 5 = 900 volts. 

To produce 900 volts and 20 amperes with a machine 
having 80°/ o efficiency, requires the expenditure of 

18,000 x -^-=22,500 watts. Of this amount 20,000 

oil 



COMMERCIAL EFFICIENCY. 197 

watts represents the internal electrical energy developed 
in the armature, and 2,500 watts represents the energy 
necessary to overcome the mechanical and magnetic 
friction of the dynamo. At 1,000 volts this energy is 
represented by a current of 2*5 amperes. A similar cal- 
culation applied to the motor gives, say, 1*5 amperes. 
We have, therefore, 

#=2-5 7 = 1-5. 

Let us assume the distance between generator and motor 
to be one mile, and the circuit to consist of two miles of 
copper wire -134 inch in diameter. At 98 per cent, con- 
ductivity the resistance of the line would therefore be 
6 '2 ohms. Allowing 3 ohms for the resistance of the 
motor, we have 

R = 14-2. 

These are all the data necessary for solving the problem 
as to current and counter-electro-motive force for maxi- 
mum efficiency. Equation 34) gives immediately 

c = 14*5 amperes, 

and 35) or 36) gives 

e = 790 volts. 

The maximum commercial efficiency attainable under 
these conditions is from equation 32) 

14-5 - 1-5 790 __ 
* = 14-5+2-5 XOOO = 6 ° P er Cent ' 

Assuming then that the generator be kept running at 
such a speed, that its electro-motive force is kept at the 
safe limit of 1,000 volts, we must, in order to obtain the 
maximum possible return of 60 per cent, of the power 
expended, so gear and speed the motor that it will oppose 
an electro-motive force of 790 volts to the current. The 



198 



ELECTRIC TRANSMISSION OF ENERGY. 



strength of the latter will then be 14*5 amperes, and 

the energy actually given out by the motor will be 

790 

-— (14*5 — 1*5) = 13'8 horse-power. 

To show how a departure from these conditions affects 
the efficiency and power developed, the following table is 
added : 



Counter-Electro- 
motive Force. 


Current. 


Commercial Effi- 
ciency, per cent. 


Power obtained 
from motor, H.P. 


790 
876 
716 


14-5 
8 
20 


60 
54 
58-6 


14 

7-7 
18 



A glance at this table will show that for currents either 
larger or smaller than 14*5 amperes, the efficiency is less 
than 60 per cent., but that the falling off is limited to a 
few per cent., whereas the power transmitted may vary 
considerably. This is a very valuable property of electric 
transmission of energy, as it allows a variation of power 
between wide limits, without serious sacrifice of efficiency, 
and thus renders the system very elastic. The great 
importance of this point will become apparent when we 
compare electric with hydraulic transmission. In the 
latter the motor consumes always the same quantity of 
water, whatever work it be doing ; and since the pressure 
is constant, the efficiency falls very low if the motor is 
working under its normal power. To remedy this, Mr. 
Hastie has introduced a water-motor with variable crank- 
radius, the latter being automatically adjusted to the 
work done by a spring. A contrivance of this nature, 
although extremely ingenious, adds considerably to the 
cost and complication of the machine and represents an 
additional chance of break-down. On the other hand, 



TWO SERIES MACHINES. 199 

electricity can be used without any separate contrivance 
for regulation, and has thus a great advantage over 
hydraulic transmission. 

The system of transmitting energy by means of two 
series-wound dynamos has the other advantage of being 
almost perfectly self-regulating as regards the speed of 
the motor. It has been shown how a motor intended to 
be worked by a constant current can be made self-regu- 
lating, that is, can be arranged to run always at the same 
predetermined speed, whatever load may be thrown on it. 
It has also been shown how motors can be made self- 
regulating, if supplied with current at constant pressure. 
In the first case, the electro-motive force must increase 
as the load increases ; and, in the second place, the cur- 
rent must increase as the load increases, one or the other 
being kept automatically constant at the generating 
station. But with a series-wound dynamo, neither the 
current nor the electro-motive force are constant, but 
vary in a certain dependence on each other. It might 
thus, at first sight, seem as if the problem of making the 
motor self-regulating were thereby rendered very much 
more difficult. This is not the case. The evil, if we may 
so regard it, in the dynamo becomes of itself the remedy 
in the motor. 

Let, in Fig. 70, O E represent the ordinary charac- 
teristic of the series-wound generator, the curve being 
drawn for a constant speed of, say, 1,000 revolutions a 
minute. Let O e represent the characteristic of the 
motor also for the speed of, say, 1,000 revolutions. The 
counter-electro-motive force developed in the armature 
of the motor at that speed is therefore represented by the 
ordinates of the curve O e. Thus to a current O C will 
be opposed an electro-motive force C 2?, to a current 



200 



ELECTRIC TRANSMISSION OF ENERGY. 



O C x will be opposed an electro-motive force C x B l9 and 
so on. In the dynamo the electro-motive force corre- 
sponding to the current O C is C D 9 and that correspond- 
ing to the current O C Y is C x D x . Draw O R under such 
an inclination to the horizontal that the tangent of the 
angle R O X represents to the scale of the diagram the 
numerical value of the sum of the resistances (R -\- r + $) 
of dynamo, motor, and line, then the electro-motive 
force lost in overcoming these resistances is for the 
current O C, evidently C A 9 for the current O C l9 C Y A l9 

Fig. 70. 




and so on. The ordinates between the straight line O R 
and the characteristic curve O E represent, therefore, the 
counter-electro-motive forces which must be developed in 
the armature of the motor at various currents. If the 
current is O (7, the counter-electro-motive force is A D, 
if the current is O C l9 the counter-electro-motive force is 
A l9 D l9 and so on. Now the counter-electro-motive force 
of the motor, if running at a constant speed of 1,000 revo- 
lutions a minute, is given by the curve O e 9 and it will 
be seen that if the ordinates of this curve are for every 
current equal to the ordinates contained between O R 



TWO SERIES MACHINES. 201 

and O E> then the motor suits perfectly the requirements 
of the generator, and it will run at a constant speed. The 
motor will run at that speed whether the current be O C x 
or O C, provided that d A x = B k D 19 and C A = B D. 

The solution of the problem consists, therefore, in the 
proper choice of motor and dynamo, so that their charac- 
teristics fit each other as nearly as possible, as explained. 
Beyond this, no other precaution or apparatus is neces- 
sary to make the system perfectly self-regulating. Even 
if the characteristics should not fulfil the condition C A 
= B D over their entire range, it will, as a rule, not be 
difficult to find two points, C x and (7, tolerably far apart, 
for which the condition is fulfilled, and between which 
the deviation of one curve from the form demanded by 
the other is very trifling. The system will, therefore, be 
practically self-regulating between these limits. Several 
years ago the author had occasion to practically test 
the soundness of this theory. He had occasion to use 
electric transmission of energy within the limits of an 
engineering works, for the purpose of supplying with 
power the pattern-makers' shop, which on account of its 
location could not be reached by any mechanical trans- 
mission. The power required by the wood-working ma- 
chines in that shop, including band and circular saws, 
was, of course, very variable, and it became a matter of 
the greatest importance to keep the main shaft — from 
which the different tools were worked by belting — re- 
volving at a constant speed. This object was attained by 
the method just described. The generator was a Burgin 
dynamo, driven at a constant speed from the main engine 
in another part of the works, and the motor was also a 
Burgin dynamo, but wound for a lower electro-motive 
force. There was a considerable distance between the 



202 ELECTRIC TRANSMISSION OF ENERGY. 

two characteristics E and O e, Fig. 70, and to find 
two points, O C x and O (7, for which the condition C A 
= B D should be fulfilled, it was necessary to increase 
the inclination of the line O R by placing a little addi- 
tional resistance into the circuit. This, of course, entailed 
some small loss of energy, but was in no way a fault of 
the system. It was occasioned simply by the necessity 
of using the two dynamos which happened to be at hand. 
If the machines could have been designed for this very 
purpose, no additional resistance would have been re- 
quired, and the automatic regulation would have been 
equally good. Within the last few years this method of 
obtaining constant motor speed in electric transmission of 
energy has been very extensively applied by Mr. C. E. L. 
Brown, formerly of the Oerlikon Engineering Works, 
Switzerland, in the various plants established by that firm 
on the Continent, and, by careful design of the machines, 
Mr. Brown has succeeded in reducing the maximum varia- 
tions in the speed of the motor between running idle and 
fully loaded to as little as 2 per cent. 

Equally good work has recently been done in this 
direction by Herr von Debrowolsky, and by the courtesy 
of this gentleman the author is able to give particulars of 
a transmission plant which he has seen tested in the 
works of the Allgemeine Elektrizitaets Gresellschaft at 
Berlin in the spring of 1890. The self-regulation 
under extreme variations of load was so perfect as to 
form the best possible proof of the correctness of the 
above theory, according to which a certain relation 
between the characteristics of the two machines insures 
constant speed of the motor at all loads, provided the 
generator is driven at constant speed. The plant in 
question consists of a 20 K. W. generator of the 



SELF-REGULATING TRANSMISSION PLANT. 203 

Edison type, working with a normal current of about 
25 amperes, a motor of the same type, and a line of 1*25 
ohms resistance. The generator is speeded at 1,000 and 
the motor at 885 revolutions per minute. The general 

Fig. 71. 



;! 



£ 






VLorv, 



iwmfYVH 



y&jwwpjz~, 







us/>t A-oiv Jje<jl J^u^/M^J^o^j^^^io^ 



■H 



1 n 1 1 1 i 




dimensions of the iron parts of the machines can be seen 
from Fig. 71, which is drawn to scale. The full lines 
refer to the generator, and the dotted lines to the motor. 
In the latter, the magnet cores are slightly smaller in 
diameter, and the yoke is also lighter. The armature 



204 



ELECTRIC TRANSMISSION OF ENERGY. 



core in both machines is 11 J- inches in diameter and 12i 
inches long, but whereas in the generator only five per 
cent, of the space is taken up by paper insulation, the 
space thus taken up in the motor amounts to twenty-five 
per cent. The winding of the armature is the same in 
both machines, and consists of 780 external conductors, 
resistance # 657. The field winding consists of 553 turns 
on each limb of the magnet, both in the generator and 
motor. The resistance of the field coils in the generator 
is 1*53 ohms, and in the motor 1*44 ohms, the reduction 
in resistance being due to the smaller diameter of magnet 



Fig. 72. 



AA/\AMMAA/WW»/WWAf\AAAMAAMAAAMA 



<$> 




&u £Z5 (OArno* 




cores. In the generator there is also a shunt of 20 ohms, 
arranged across the terminals of the field coils. This 
shunt is a resistance coil made of wire doubled back on 
itself, so as to have no self induction. It will be obvious 
that by the addition of such a shunt any slight error in 
the design of the machines can be rectified, that is to say, 
a more perfect agreement between their characteristics 
obtained ; but according to Dobrowolsky the shunt does 
more than this, it increases the rapidity with which one 
machine corresponds to the other. If the load on the 
motor be suddenly diminished, the current will be as 



SELF-REGULATING TRANSMISSION PLANT. 205 

suddenly checked ; but very rapid variations of current 
through the fields are resisted by the self-induction of 
the magnets. There must thus always be a tendency to 
irregularity in the speed owing to a kind of surging of 
energy to and fro between the two machines, which 
according to the degree of disturbance will take a longer 
or shorter time to die out. By the adoption of the shunt, 
which acts as a kind of electro-magnetic damper or dash- 
Fig. 73. 




gKernSLne. 



pot, the kick from the magnets is principally taken up by 
the shunt, and the machines are thereby able to attain 
more quickly their steady working condition. 

Fig. 72 shows diagramatically the arrangement of 
circuits. As it might break down the insulation if the line 
were opened by an ordinary switch, the stopping of the 
current is effected by means of a switch S 9 which is con- 
nected with the terminals of the field coil on the gene- 
rator. By closing this switch the field is caused to 
vanish, and the current gradually stopped. A liquid 



206 ELECTRIC TRANSMISSION OF ENERGY. 

rheostat serves for starting the motor. This is shown in 

Fig. 74. 




Fig. 73. It consists of a series of vessels filled with five 



STARTING DEVICE. 207 

per cent, soda solution, into which dip iron electrodes A 
attached to a cross beam B, which can be raised and 
lowered by means of a crank, rack, and pinion. The 
electrodes are shaped as shown at A 1 . In the vessels 
there are fixed strips of iron of the form shown, with 
knife contacts at either end of the apparatus, and when 
the movable electrodes are placed right down the knife 
contacts short circuit the electrodes. To prevent creeping 
the upper parts of the iron plates are painted with some 
heavy mineral oil. The iron is not attacked by the cur- 
rent. For pressures up to 200 volts, Herr von Dobrowol- 
sky uses in his liquid rheostat two vessels only, and for 
pressures up to 800 volts he uses four vessels. 

The curves, Fig. 74, show the results of tests with the 
transmission plant above described. The inclined straight 
line represents the loss of electro-motive force due to the 
resistance of the circuit, and the two curves represent 
dynamic and motor electro-motive force of the two 
machines respectively. The line at the top of the 
diagram shows the speed of motor actually observed at 
various currents. 



CHAPTER VII. 

Importance of alternating currents for long distance transmission — Ideal 
Alternator— E. M. F. of Alternators— Effective E. M. F. and Effective 
Current — Clock Diagram — Self-induction— Power — Different Methods 
of measuring Power. 

The problems treated in the previous pages had reference 
to the use of continuous currents only, and in the early- 
days of electric power transmission, dynamos and motors 
of the continuous current type were the only machines 
considered practicable for the purpose. As, however, 
the science of electrical engineering advanced, it began 
gradually to be perceived that alternating currents might 
also be used for working electro motors, and this branch 
of the subject has within the last two or three years been 
developed with even greater rapidity than the older 
branch of continuous current work. 

There have been principally two causes which have 
led to this development. In the first place the desire to 
augment the earning capacity of existing alternating 
current central stations by the sale of current for power 
purposes in addition to its use as a lighting agent, and in 
the second place the natural growth of transmission plant 
up to and beyond the limits suitable for continuous cur- 
rents. The first of these causes tended to the invention, 
design and perfecting of motors of small or moderate 
power capable of being worked on the existing systems 
of distributing mains in towns and the other to the 



IMPORTANCE OF ALTERNATING CURRENTS. 209 

development of alternating current generators and motors 
of large power in combination with extra high, pressure 
transmission plant suitable for long distance work. The 
question might perhaps be asked, why for such work 
continuous current plant could not equally well be used. 
The principal reason is the difficulty of obtaining that 
degree of insulation in dynamos and motors which is 
required to withstand the extra high pressure. It has 
been shown in the previous chapters that the higher the 
line resistance, that is, the greater the distance to which 
the power has to be transmitted, the higher must be the 
working pressure in order to secure a satisfactory degree 
of efficiency. To reduce the line resistance by increasing 
the area of the conductor in order to reduce the working 
pressure is of course always possible, but it is not always 
financially right, because in so doing we have to increase 
the capital outlay for the line too much. It is quite 
conceivable that the annual interest and depreciation on 
the line would in such a case approach or even exceed 
the cost of the power if it were produced by an engine 
at the receiving end of the line, and under these circum- 
stances electric transmission would be commercially a 
failure. Obviously, a liberal use of copper in the line is 
no solution of the problem how to carry power to long 
distances ; the only practicable solution is the employ- 
ment of high or extra high pressure. As the distance of 
transmission increases, we thus arrive eventually at a 
pressure for which continuous current machines cannot 
easily be insulated. The chief difficulty lies in the 
commutator. Here we have an organ composed of 
metallic sections which are necessarily devoid of insula- 
tion on the outside, and are therefore subject to surface 
leakage. The armature conductors themselves can of 

V 



210 ELECTRIC TRANSMISSION OF ENERGY. 

course be insulated to any desired degree, but as their 
ends must be connected with the plates in the commu- 
tator, there is introduced an element of weakness which 
lowers the insulation of the machine taken as a whole. 
With alternators the case is different. Since these 
machines have no commutator, it is possible to design 
them in such way that no portion of the armature circuit 
contains any exposed metallic part, and there is no 
danger of surface leakage. The whole of the armature 
circuit may be highly insulated, and thus the working 
pressure may be made much higher. It is hardly pos- 
sible to assign an exact limit of pressure at which the 
continuous current dynamo begins to become impractic- 
able. This depends largely on design, material and 
workmanship. When no special precautions are taken 
in the design, but sound material and high-class work- 
manship are employed, machines for 2,000 volts and 
even 3,000 volts are fairly reliable. With special designs 
insuring the insulation of the armature and commutator 
from the shaft, the magnets from the bedplate, and the 
latter from the foundation, combined with very careful 
workmanship, even higher pressures can be obtained ; but 
whatever may be the limit, it cannot be so high as with 
alternators, whilst the cost of the machine, owing to these 
special precautions, becomes high. With alternating 
currents we have the further advantage that the machine 
itself need not be subjected to any high pressure at all. 
We can always employ transformers to increase or 
reduce the pressure in any desired ratio, and as these 
transformers contain no moving parts, they can be insu- 
lated to any extent we please. Alternating currents are 
therefore eminently suitable for long distance transmis- 
sion, and it will now be necessary to place before the 



E.M.F. OF ALTERNATOR. 



211 



reader a short outline of the the theory of alternating 
current apparatus. 

An ideal form of alternator has already been shown in 
Fig. 13, here reproduced. The E.M.F. induced in a 
uniform field F is 

E—F d co sin a, 

Fig. 75. 




where a is the circumferential speed of the wire sweeping 
through the field F, and d its length. At the moment 
when the plane of the coil is parallel to the lines of the 



7T 



field « = -, and the E.M.F. generated attains its maxi- 

mum value of F d co. It will be convenient to alter this 
expression by introducing the dimensions of the coil 
and its rotary speed. Let the symbol ~ represent the 
number of revolutions made by the coil in one second, 
thus: 

CO — 2 7T r ~. 

E— 2 7T ~ F r d sin a. 

Now F is the strength of the field expressed in number 
of lines per square centimeter, and F r d is therefore the 
total induction or total number of lines passing through 
the coil when the plane of the latter is at right angles to 



212 ELECTRIC TRANSMISSION OF ENERGY. 

the direction of the field. This quantity we have denoted 
by the symbol z in the formulas for dynamos. Retaining 
the same notation we have therefore 

E=2 ~ 7T z sin oc 

as the instantaneous value of the E.M.F. in a coil of one 
turn containing two active wires. In a coil of two turns 
there would be four active wires, and the E.M.F. would 

be double the above amount ; whilst in a coil of - turns 

containing t active wires we would obtain 

E = t 7T ~ Z sin a. 

This is the E.M.F. induced in the coil at the moment 
when its plane includes the angle a with the position 
of zero E.M.F. when the coil stands at right angles to 
the lines of force. As a increases from zero to 2 vr, the 
E.M.F. passes through a complete cycle, attaining a 

positive maximum for a = -t, then falling to zero at cc = 7r ; 

3 

after that attaining a negative maximum for a = - tt, and 

becoming zero again for cc = 2 tt. It is obvious that 
this periodic variation of E.M.F. can be represented 
graphically by the projection O e of a line O E (Fig. 76), 
revolving round O at a speed of ~ complete revolutions 
per second. If we suppose the radius O E to represent 
the plane of the coil, and the lines of the field to be vertical, 
then the maximum E.M.F. will be generated when the 
revolving line O E is vertical (plane of coil parallel to 
lines of force and active wires cutting them at right 
angles, therefore at maximum rate), and the angle a has 
to be reckoned from the horizontal. A diagram of the 



CLOCK DIAGRAM. 



213 



kind shown in Fig. 76 is called a " clock diagram " on 
account of the resemblance of the motion of the radius to 
that of the hand of a clock, and it is obvious that we 
may represent not only an E.M.F., but also a current in 
the same way, provided it varies according to a sine law, 
such as 

i=I sin a, 

where i is the instantaneous value of the current, and / 
its maximum value. Thus imagine the terminals of the 
coil in our ideal alternator connected to a voltmeter of 

Fig. 76. 




the hot wire pattern, then the current flowing through 
the wire must at any instant be proportional to the value of 
the E.M.F. The total work dissipated in heat during one 



cvcle is in this case 



/ 



E 2 
R 



sin 



a 



dt \ if by E 



we now denote the maximum value of E.M.F., by R the 
resistance of the voltmeter, and by T 7 , the time of a com- 
plete cycle. Since a = 2 tt ~ t, the integral may also be 
written thus : 



214 ELECTRIC TRANSMISSION OF ENER G F. 

T 

i)d(2 7r ~ t). 



E 2 I 

r= / Si7l 2 (2 7T ~ 

*~RJ 



This is the work dissipated in the time T= — To 

find the rate per second at which work is dissipated, we 
must multiply with ~ and have 

T 



J" 



TT' 2 

w=- h- / sin 2 (2 7T ~ t) d(2 7T ~ t). 

Ji 7T It 





The solution of an integral of the form/ sin 2 a d ah 
a sin a cos a 
2 2 * 

The second term cancels out because sin a is zero for 
either limit, and we have 

E 2 2tt 



w = 



2 7T R 2' 
E 2 



w 



2 R 

If the same voltmeter had been connected to the 
brushes of a continuous current dynamo giving an 
E.M.F. e, the power dissipated would have been 



e 
W = R' 

Both machines will therefore give the same deflection 
on the voltmeter, or the same light in a glow lamp if 

2 

e=-§ ....... 38) 

</ 2 



EFFECTIVE PRESSURE. 215 

We thus find that the volts measured at the terminals 
of our ideal alternator compared to its maximum volts 

are in the ratio of 1: \/ 2 ; or in other words the alter- 
nating volts which produce the heating effect in a wire or 
lighting effect in a glow lamp amount to 70*75 per cent, 
of the maximum volts induced in the coil. This pressure 
is called the " effective " or " virtual " pressure. 

We can now compare the effective pressure produced 
by our ideal alternator with the pressure which would 
be produced by a continuous current dynamo, having the 
same speed, total field, and number of active conductors 
on the armature. 

The effective E.M.F. produced by the alternator is 

1 

e a = — i 7T Z T ~ 

v 2 
and that produced by the continuous current dynamo is 

e c = z t ~. 

The two are in the ratio of y-?: 1 or very nearly. 

e a = 2-22e c . 

That is to say, to obtain the voltage of the alternator 
we calculate the E.M.F. as if we had to do with a 
dynamo and multiply the result with 2*22. This is, how- 
ever, only correct for alternators in which the wave of 
induced E.M.F. follows strictly a sine function. The 
shape of the curve obtained in practice differs to some 
extent from the true sine curve, and the co- efficient instead 
of being 2*22 may have some other value. Let this 
value be K, then the general formula for the E.M.F. of 
an alternator is 



216 ELECTRIC TRAKS31ISSI0N OF ENERGY. 

The exact value of the co-efficient K depends on the 
shape and configuration of the armature coils and magnet 
poles, but it does not vary within very wide limits. For 
most modern and well designed machines K lies between 
2*00 and 2*30. In certain cases, notably with toothed 
armatures producing a very peaky E.M.F. curve iTmay 
rise as high as 2*60. 

The above formula gives the E.M.F. of an alternator 
having'two poles only. If there are more poles and the 
armature coils are coupled in series, the E.M.F. is cor- 
respondingly increased. Say that we have a machine 
with p pairs of poles (2p poles) then the E.M.F. would 
be p K z t ~ 9 z being again the total induction due to 
one pole and its fellow. Let n be the speed of the 
machine in revolutions per minute then n/60 is the speed 
per second. The number of complete cycles through 
which the E.M.F. passes per second is therefore p times 
n/60 or 

p n 
~ = 60~ 

which inserted in the above formula gives 

e=pKzr- 

in absolute measure. To obtain the E.M.F. in volts we 
multiply by lO 8 , and have 

e=p Kzt^ lO 8 ..... 39) 

It is important to note that z must be inserted in 
absolute measure, and represents that induction which 
passes through one coil alternately in one and in the 
opposite direction. When the induction does not vary 



3IEASURING POWER. 217 

from + z to — z, but only from + to z zero and back again 
to -f- Z, as in the Mordey machine, the E.M.F. is obviously 
only half that given by the above formula. It should 
also be noted that t does not mean the number of turns 
of wire on the armature, but the number of active wires 
when counted all round the circumference of the armature, 
precisely as in the case of dynamos. 

If we give z in English measure, the E.M.F. of an 
alternator in volts is 

e=p Kz rrc 10 G 40). 

It is now necessary to investigate the power represented 
by an alternating current. With a continuous current 
the problem is simple enough ; we have only to multiply 
amperes and volts to get the watts expended, but with an 
alternating current this method of computing power is 
not generally admissible, because the current curve does 
as a rule not coincide with the E.M.F. curve. To see 
this clearly let us suppose an alternating current sent 
through the circuit, shown in Fig. 77, which consists of 
an alternator, A, an electro-magnet, B, and a bank of 
glow lamps, G. v, v x and v 2 are voltmeters of the electro- 
static type, i.e. instruments which take no appreciable 
current. In order to simplify the problem we assume 
that only the bank of lamps has ohmic resistance, which 
we call r. 

The current passing through the electro-magnet will 
energize it. Let the core be made of laminated iron so 
that the magnetization may instantly follow the exciting 
power, and let the iron be of such good quality that no 
appreciable amount of power shall be wasted in the 
process. Let F be the total induction produced when 
the current i has its maximum value / and t the number 



218 



ELECTRIC TRANS3IISSI0N OF ENERGY. 



of turns of wire through which the flow of lines passes. 
If the current passes through ~ complete cycles per 
second, or, as it may also be expressed, if it has a frequency 
~, the coil will in respect to the field created by its own 
current be in exactly the same condition as the coil of 
our ideal alternator (Fig. 13), is in respect of the field 
produced by the system of field magnets. We have seen 
that when the plane of the coil is at right angles to the 
lines of force, that is, when the total induction passing 
through the coil is a maximum, the E.M.F. is zero, and 
when the coil had turned through 90° so as to bring 

Fig. 77. 




e 



/ iro v 



<?$$<?<? g >~ 



its plane parallel to the lines of force, making the flux 
through it zero, the E.M.F. is a maximum, namely 
2 7T ~ F for each turn of wire. The electro-magnet B 
has t turns of wire and the maximum value of the E.M.F. 
induced in it, when the flux, and therefore the current 
producing this flux pass through zero, is 

F s = 2tT ~ T F, 

This is called the E.M.F. of self-induction, because it 
is produced by the current itself. Obviously, the total 
flux F is a function of the current, and since E s is propor- 
tional toi^, the E.M.F. of self-induction must be a func- 



E.M.F. OF SELF-INDUCTION. 219 

tion of the current. If the core of the electro-magnet be 
magnetized only to a low degree, say not beyond 5,000 
or 6,000 lines per square centimetre, then the permea- 
bility may, without serious error, be considered as con- 
stant for all points of the magnetic cycle, and in this 
case the instantaneous value of F would be proportional 
to i 3 and the maximum value to be inserted in the 
above formula would be proportional to /. We 

4 7T I T 

have, in fact, F=p a, where / is the length, a the 

V 

area of the magnetic circuit, and p its permeability. If 
we put 

(A 4 7T a t 2 



we have also 



l - i 

JE=2 7T ~ L L 



In this equation /and E s are given in absolute measure. 
If we wish to have them in amperes and volts we must 
divide the right hand side by 10 and by 10 8 . 

Volts of self-induction 

JE S = 2 n ~ L J10 9 . 

L is called the co-efficient of self-induction, and from 
the equation above given it is obvious that it must be a 
length. This equation contains on the right-hand side 
only numerics (4, tt, t 2 , and //) and the ratio a/l, which is 
an area divided by a length. This must obviously be a 
length, and as all our formulas are based on the c. g. s. 
system, this length must be given in centimetres, and the 
unit of the co-efficient of self-induction in the c.g.s. system 
must therefore be the centimetre. This, however, is too 
small a unit for convenient practical use, and a unit a 



220 ELECTRIC TRANSMISSION OF ENERGY. 

thousand million times as great has been adopted. This 
is called by the following names: (1.) The " Secohm," 
from the fact that a length may be considered as the 
product of a velocity (ohms), and a time (seconds). (2). 
The " Quadrant," from the fact that 10 9 centimetres re- 
presents very nearly the length of an earth quadrant. 
(3). The " Henry," in honour of the American electrician 
of this name. The last name for the unit of self-induc- 
tion seems at present to find most general adoption, 
having been recommended by the Chicago Electrical 
Congress. 

If then we give L in henry s the factor 10" 9 must be 
omitted, and we have the maximum E.M.F. of self-induc- 
tion in volts. 

Es = 2 7T ~ L I 41) 

/ being the maximum value of the current (crest of 
current wave) in amperes. The effective volts of self- 

Es 

induction are of course — -, and since effective and 

V2 
maximum current stand to each other in the same rela- 
tion of 1 : \^2 y Ave find the effective volts of self-induc- 
tion by simply inserting the effective instead of the maxi- 
mum value of the current. 

e s = 2w~Li 42). 

If we have to do with a continuous current, c, the 
E.M.F. required to force it through a resistance, r, is e = 
r c. Now the E.M.F. required to force the alternating 
current through a coil having self-induction, is given by 
a formula of similar construction. We have i for alter- 
nating current instead of c for continuous current, and 
instead of a resistance r given in ohms we have- the term 
2 7T ~ L. This must be the equivalent of a resistance 



INDUCTANCE. 221 

as we can easily see from the fact that L is a length and 
~ is the reciprocal of a time ; therefore ~ L is length 
divided by time, which means a velocity. The expres- 
sion 2 7r ~ L has therefore the same dimensions as a 
velocity, and as a resistance has also the same dimen- 
sions, we find that 2 tt ~ L represents a resistance. It 
is, however, a kind of resistance which does not absorb 
power, and to distinguish it from a true ohmic resistance 
it is called " inductance." 

Let us now see how the relation between current and 
E.M.F. of self-induction can be represented in a clock 
diagram. In the first place it will be obvious that the 
current line must always be at right angles to the E.M.F. 
line, for only then is it possible that the projection of one 
is zero at the moment when the projection of the other is 
a maximum. There remains only the question how the 
direction of current and E.M.F. shall be represented in 
the diagram. Let us agree to call a current positive when 
it passes through B (Fig. 77) from left to right, and let 
us call in the clock diagram a current positive when the 
projection of the current line is above the centre. As- 
suming that the lines revolve clockwise, and that we 
start counting the angle of rotation from the horizontal 
position of the current radius to the left, then cur- 
rents corresponding to all the angles between a = o and 
a = tt would be positive, and currents corresponding to 
all the angles between a = tt and a = 2 tt would be 
negative. 

Similarly we call an E.M.F. generated in the coil posi- 
tive when it tends to produce a positive current, i.e. 9 a 
current flowing from left to right. Now it is obvious 
that the- E.M.F. of self-induction must, on the whole, 
tend to prevent both the growth and the decrease of the 



222 



ELECTRIC TRANSMISSION OF ENERGY. 



current, in other words, it must tend to diminish the 
amplitude of the current wave, for were it to increase the 
amplitude it would be opposed to Lenz's law. We thus 
find that at the moment when the current passes through 
zero and becomes positive, the E.M.F. of self-induction 
must act in B from right to left, that is, it must be nega- 
tive. The machine A must therefore at this moment 
impress upon the coil an equal and opposite E.M.F., 

Fig. 78. 




appearing in the diagram, Fig. 78, as a vertical line OE s 
in the upper or positive half of the figure. The current- 
line at this moment is 01. The voltmeter v± placed 
across the terminals of the coil B will therefore show the 
effective voltage which the machine must impress upon 
this coil in order to balance its E.M.F. of self-induction. 
But the machine must do more. It must also supply the 
volts required to drive the current through the lamps. 
Since the latter have only ohmic resistance, the lamp 



ANGLE OF LAG. 223 

volts and lamp current must coincide in phase, and their 
relation is correctly represented by Ohm's law. Let E r 
be the volts required to send the current 1 through the 
resistance r, then 

E r — r /and 

e r = r i, 

which voltage is measured by the voltmeter v. 2 . In the 
diagram the maximum lamp voltage is represented by the 
horizontal line O E r . The machine has then to give not 
only the E.M.F. QE„ but also the E.M.F. O E r . Com- 
bining the two in a parallelogram of forces, we thus find 
that the machine must impress on the whole circuit the 
maximum voltage of O E. The diagram was developed on 
the assumption that the lines revolve clockwise. The 
volt line O E will therefore pass through the vertical 
position before the current line, that is to say, the 
maxima of volts and amperes given by the machine do 
not coincide, but the amperes lag behind the volts by a 
certain amount represented in the diagram by the angle 
<p. This angle is called the "lag," or " angle of lag." 
We have assumed that no power is expended in coil B, 
so that the whole of the power coming out of the machine 
is given to the lamps, and amounts to 

. IE, 

w = ie r = — - 

In the diagram the energy expended is therefore repre- 
sented by half the area of the shaded rectangle, or if we 
had drawn the diagram so that the different lines repre- 
sent not the maximum, but the effective values of the 
different quantities, the energy would be represented by 
the area of the shaded rectangle. Since O E r — O E 



224 ELECTRIC TRANSMISSION OF ENERGY. 

cos <p, it follows that the equation for the power may 

also be written thus — 

IE cos (p 

»=— a— ■ 

or, when effective values are taken, 

w = i e cos (p ..... 43) 

To find the power given out by the alternator in watts, 
we have therefore to multiply the effective amperes by 
the effective volts and by the cosine of the angle of lag. 
It is interesting to inquire for what resistance in the 
lamp circuit this power becomes a maximum. From 42) 

we have z = - — ^, which inserted into 43) gives 

e s e cos (p 
w = - 



7T 



~ L 



Since the self-induction of the coil does not vary, 2 tt ~ L 
is a constant, and the power is proportional to e s e cos 
(p = e s e r . The problem then is to find that position of E 
on the circle marked " machine volts," for which the 
product e s e r becomes a maximum. Obviously this will 
take place when the line O E includes an angle of 45 deg. 
with the horizontal, for which position e s =e r . We obtain 
maximum power when the volts of self-induction equal 
the volts applied to the lamps, that is, when the resistance 
of the lamps has the value r = 2 tt ~ L. 

The lag in this case is 45 deg. 

It will be seen from the diagram that 



2 ° . S 

e =e r +e s 



since e r — i r, and e s — i 2 tt ~ X, we have also 

e 2 = i 2 {r- + (2 7r ~ Z) 2 ), 



IMPEDANCE. 

from which we find the current 



225 



z = 



</r 2 + (2 7r ~ Lf 



44). 



This formula enables us to predetermine the current 
when the frequency, E.M.F., resistance, and self-induc- 
tion of the circuit are given. The analogy with Ohm's 
law is apparent at a glance. In the formula expressing 
Ohm's law the denominator is simply a resistance ; here 
it is the square root of the sum of two terms, one being 
the square of the resistance, and the other the square of 
the inductance. The denominator in 44) is called the 

Fig. 79. 




"impedance," and may, according to Dr. Fleming, be 
represented as the hypothenuse of a right-angular tri- 
angle, the sides of which represent resistance and in- 
ductance as shown in Fig. 79. 

In the above investigation we have arrived at the 
principle according to which the power given to a 
current must be computed ; and it is now necessary to 
show how this principle can be applied in practice. In 
the case represented by Fig. 77 there is no difficulty in 
measurirfg the ptfwer given by the alternator. We 
have sftnply to determine that passing through the 
lafrvps in the usual way. But this is only correct under 
the supposition that the coil B does not absorb any 
power at all, a condition not attainable in practice. 

Q 



226 ELECTRIC TRANSMISSION OF ENERGY. 

Let us now see how the power given out by the alter- 
nator can be correctly measured if the coil B, besides 
having self-induction, also has a certain, but unknown 
resistance, by virtue of which it absorbs power. We 
can even go further, and assume that B absorbs power 
not only on account of its ohmic resistance, but because 
it does useful work in some form or other. It might, 
for instance, be the primary coil of a transformer or 
the armature of an alternating current motor. What- 
ever be the kind of work done in B it is clear from what 
has already been shown that the true watts supplied to B 
are the product of the current and that component of the 
E.M.F. which coincides in phase with the current. But 
when an E.M.F. coincides in phase with a current the 
two are in a relation correctly represented by Ohm's 
law, and we may therefore represent any kind of useful 
work by the equivalent of an inductionless resistance 
which is heated by the current. For the sake of sim- 
plicity we will adopt this method of representation, 
assuming that for the transformer or motor or other 
apparatus we substitute a coil B, which has the same 
co-efficient of self-induction and a resistance so adjusted 
that the energy absorbed in it shall be exactly equal to 
the energy which would be given to the transformer, 
motor, or other apparatus which it replaced. 

Let r Y represent this unknown resistance of i?, and 
r 2 that of the bank of lamps, then i 2 r Y is the energy 
absorbed by the coil, and i 2 r 2 that absorbed in the lamps, 
the energy supplied by the machine being i 2 (r x + r 2 ). 
Taking in all cases effective (not maximum) values, we 
find by the voltmeter v x the E.M.F. over the terminals 
of the coil B. Let this be e^ and let e % be the E.M.F. 
over the lamps. The E.M.F. taken at the terminals of 



THREE VOLT METER METHOD. 



227 



the machine we call e. The E.M.F. e Y may be con- 
sidered to be made up of two components ; one e in 
phase with the current, and therefore equal to ir l3 and 
the other e s due to self-induction and in advance over 
the current by 90°. Let, in Fig. 80, OB represent e i 
then 0(7 is the E.M.F. of self-induction e s , and OA = e\ 
Similarly let OG represent the terminal E.M.F. of the 
machine, and OD that component of it which is in phase 
with the current. There being no self-induction in the 
lamps, the hight of the point G over the horizontal must 
be the same as that of point B. Since the E.M.F. over 




the lamps must be in phase with the current and with 
e we have 

e 9 + e 2 = OD, 

and find that the following relations exist : 



,' 2 



By eliminating e s we obtain 



e~ — e l ~ — e. l ~ 



2 e 2 
The energy w l in coil B is e'i, and we find thus 

• / 2 2 2\ 

i (e —e, —e<>) 



. . 



45). 



228 



ELECTRIC TRANS3IISSI0N OF ENERGY. 



The determination of the energy requires therefore 
three measurements of E.M.F. and one current measure- 
ment. The latter may be omitted if the resistance r 2 of 
the lamps or other non-inductive resistance is accurately 



known. 



Since i = — we can also write 
r 2 



w,= 



2 2 2 

e e \ e 2 



2 r, 



46), 



For practical work the equation 45) is preferable to 
46), because the exact resistance of G, especially if this 
part of the circuit consists of glow lamps, is not easily 
determined. This method of determining the power 
given to an alternate current circuit has been devised 
by Professor Ayrton and Dr. Sumpner, and is known 
as the " Three Voltmeter Method." To ensure accuracy 
it is advisable to make all these volt-measurements with 
the same instrument, by using suitable connections and 
switches. It is also advisable to so adjust the non- 
inductive resistance that e 2 becomes approximately equal 
to e x . If there is a large difference between the two, 
then a small error in the measurements of E.M.F. leads 
to a large error in computing the power. The power 
given by the machine is the sum of that given to the 
coil and that given to the lamps. 



w = w l + i e % 
2 " 



10 



10 = 



*2 



x,2 I „ 2 „ 2 



2 r. 



. 47), 
. 48), 



It has already been stated that to obtain accurate 
results e l should not differ very much from e 2 ; this con- 



THREE AMPERE METER METHOD. 



229 



dition implies that e should exceed either by about 40 per 
cent., and where the object of measurement is to find the 
total power supplied by the machine, the apparatus 
may generally be so adjusted as to satisfy this condition. 
All we need do is to work the transformer or motor B 
at a lower voltage than that of the machine. But if the 
problem is to determine the power taken by the trans- 
former or motor B, then we must work it at the voltage 
for which it has been designed, and the alternator must 
be worked at a higher voltage. When this is not 
practicable a modification of the three voltmeter method 




may be used. This was devised by Dr. Fleming, and is 
known under the term " Three Ampere Meter Method.'' 
Its application will be understood on reference to Fig. 81, 
where A is the alternator, and «, a Y and a 2 are ampere- 
meters indicating respectively the total current and its 
two components which pass through coil B and lamps G. 
An investigation analogous to that given with reference 
to the previous method (but which for want of space is 
omitted), shows that the power given to the coil is 

/ «2 • 2 • 2\ 

e_ (i — i L —z 2 ) 

2 



W?l= TT 



49). 



e being the terminal voltage of the coil. If the re- 



230 ELECTRIC TRANSMISSION OF ENERGY. 

sistance r. 2 of G is accurately known, the voltage need 
not be measured, since the power is also given by the 
formula 

m?i = -|-(« 2 — i\— 4*) .... 50). 

Both methods of power-measurement here explained 
have the disadvantage that an amount of power compar- 
able to that to be measured must be wasted in a non-in- 
ductive resistance. There is no difficulty in constructing 
such a resistance capable of taking up a small amount of 
power. A bank of glow lamps does very well. for this 
purpose ; and where we wish to measure the power lost in 
a transformer when working on open circuit, or that lost 
in a motor when running light, either of the two methods 
may usefully be employed. But when it becomes neces- 
sary to measure the output of a large alternator amount- 
ing to some 100 kilowatts or more, an inductionless 
resistance if it were composed of glow lamps would be- 
come cumbersome and costly. We must, therefore, 
employ some other kind of resistance. If metallic, we 
cannot be sure of its being inductionless, and thus the 
three voltmeter and the three amperemeter methods be- 
come alike uncertain. A practical way of measuring 
consists in employing a metallic resistance formed by 
wire or strip which is wound, not spirally, but zig-zag 
fashion on a frame so as to make it as nearly as possible in- 
ductionless. The material employed should have as small 
a temperature coefficient as possible (manganese-steel or 
platinoid are very suitable alloys), and the total capacity 
of the resistance should be large enough to take the 
whole of the power without excessive heating. To find 
the output of the machine, the current is sent through 
this resistance and is measured when the latter has 



LARGE RESISTANCE FRAME. 231 

reached a steady temperature. The current is then 
Itupted, and'the resistance of the frame » aken 
at eertain intervals of time, the observations being plotted 
show by a curve the rate at which the instance de- 
ceases as the frame becomes cooler. This curve pro- 
ved backwards to the moment when the current wa 
interrupted, gives with a high degree of accuracy the 
resistance of the frame when the measured current wa, 
flowing through it, and the power is then found by multi- 
plying the square of the current with tins resistance. 
P This method of measurement is very suitable for the 
workshop, before the machine is sent out. It may occa 
sionally be applied to machines after erection but the 
necessity of using large resistance frames .and dehcate 
instruments for measuring resistance renders it lathe 
cumbersome, whilst it is of course quite unsuitable to a 
cases where the electric power to be measured is that put 
into (and not that taken out of) the machine. 

What is required for general use is a method which 
can be applied equally well in any local*, , and whuA 
does not itself absorb any appreciable amount^ of powei. 
An instrument which complies with these requirements is 
the wattmeter. This is constructed similarly to an 
ordinary current dynamometer, but instead of passing the 
^ne current in series through both coils, the current of 
Xch the power is to be measured is passed through one 
of the coils, and the other coil forms a shunt across the 
terminals o the apparatus under test. If necessary, an 
additional resistance may be inserted in this sW circu£ 
Before entering on the theory of the wattmetei,it will be 
exped ent to consider the action of the instrument when 
21 as a dynamometer with an alternating current. 
Snce the direction of the current changes simultaneously 



232 ELECTRIC TRANSMISSION OF ENERGY. 

in both coils, the force, which tends to deflect the mov- 
able coil, acts always in the same direction. It is, how- 
ever, a variable force changing from zero to a maximum 
2 ~ times a second, being, of course proportional to the 
square of the current at r any instant. If the spring and 
movable coil had no mass, the latter would oscillate 
under the influence of the cuirerit, but as it has a 
considerable mass compared with the force acting on it, 
and as the frequency with which the force comes and 
goes is comparatively high, the movable coil can be kept 
steadily in the zero position by turning the pointer in the 
same way as if the current were continuous. The 
acceleration given by a force,/*, to a mass, m, is f/rri, and 

T 

the speed attained after T seconds is / — dt, the mass 

Jo m 

being supposed to be at rest at the moment from which 
the time is counted. In our case the value of the 
integral is zero, since, owing to the weight of the coil, no 
movement and, therefore, no speed is imparted to it. We 



have, therefore, the condition of equilibrium— / f dt 






I sin OL 

— o, where f = — j™ — • K is the co-efficient of the 

instrument obtained by calibration with a continuous 
current, when the force is given by the deflection of the 
pointer. Calling this Z>, and the continuous current 
c, we have c = Ka/j) an( j w ith an alternating current we 

have DK 2 = — - I I 2 sin 2 a dt. The value of the right- 






D YNAMOMETER. 233 

P 

hand term, as already shown, is — = i 2 and we find there- 
fore that 

This is precisely the same formula as with a continuous 
current, and we see that a dynamometer calibrated on a 
continuous current may be used for the measurement of 
an alternating current, and will give the effective value of 
the current. 

Now let us see how this instrument may be arranged 
to measure power. As usually made, the dynamometer 
has an internal connection between the two coils not 
accessible to the user. There is thus only one external 
terminal for the movable coil and one for the fixed coil* 
Generally there are two fixed coils, in order to obtain a 
greater range, and then three terminals are provided. 
For the sake of simplicity we shall however assume that 
we have to do with an instrument having only one fixed 
coil, and to avoid complication in the diagram we show 
the movable and fixed coil to consist of one turn each, 
though in instruments as actually made, any number 
of turns may, of course, be used. Let, in fig. 82, C 
represent the movable and c the fixed coil, whilst dfis 
the internal connection, leaving only the terminals 7\ T. 2 
accessible. If the instrument be inserted in the usual 
way, the current coming in at T x and going out at T 2 will 
traverse both coils in a clockwise direction, and produce 
a defective force on C which can be balanced by moving 
the pointer in the direction intended by the maker of the 
instrument. Movement in the opposite direction is 
generally prevented by a stop. If the currrent comes in 
at T 2 an( l g°es out at T x the direction of current is reversed 



234 



ELECTRIC TRANSMISSION OF ENERGY. 



in both coils and the mechanical effect is the same as before. 
Since the deflection must always be taken in the same sense, 
it is of course necessary when altering the connections of 
the instrument to take care that whatever currents be flow- 
ing through the coil they must traverse them in the same 
sense, that is, either both clockwise or both counter-clock- 
wise. Let us now attach a third terminal, T 3 , to the con- 
nection df and insert the instrument into an alternating 
circuit as shown. A is the alternator, B is the apparatus 




the power given to which is to be measured, R is an in- 
ductionless resistance which may conveniently consist of 
glow lamps arranged in series, and a is an amperemeter. 
The fixed coil and resistance R form a shunt to B, and it 
is obvious that the currents will pass through C and c in 
such sense as to produce deflection of the movable coil in 
the desired direction. If we include the resistance of the 
fixed coil and amperemeter in the term R, and assume 
that the movable coil C has only a negligible resistance, 
and that the self-induction of either coil is also a negligible 



WATT METER. 235 

quantity, we find that the current i passing through c is 
in phase with the E.M.F. e impressed on B and that it is 
given by the expression : 

• L_ e 

The current / through the movable coil acted on by the 
field due to i produces a deflecting force, the instantaneous 
value of which is proportional to 

I sin (ot — (p) i sin a, 

<p being the angle of lag and I 0} i the maxima of the two 
currents. Substituting for i its value eJR the force pro- 
ducing the deflection D is 



DK 2 = A — / 



sin (# — <p) — e sin a dt, 
R 



T 

I sin {a — <p) e sin a. dt, 



If we were to draw a clock diagram to represent the pre- 
sent case we would have an E.M.F. e leading before a 
current I by the angle <p, the power represented being, as 

already shown, W = S-t cos <p. Instead of the integral we 

At 

can therefore also write 

DK 2 = 1 111* cost, 
R 2 

and since I„ = 1^/2 and e = e y/2 we can also write 

DK 2 = ~ Ie costp 51). 

R 



236 ELECTRIC TRANSMISSION OF ENERGY. 

The power passing through the wattmeter is I e cos <p, or 

W= RDK 2 52). 

K being, as before, the coefficient of the instrument ob- 
tained by calibrating it as a dynamometer on a continuous 
current. The expression 52) can only be used if the resis- 
tance R is accurately known. This may be the case where 
the resistance consists of platinoid wire or a similar mate- 
rial having a very small temperature coefficient, but when 
lamps are used the resistance varies so much with the cur- 
rent that for accurate work it is necessary to determine it 
for each reading. We have then to observe e on a volt- 
meter v, and i on an amperemeter a, inserting into 52) for 
R the ratio e/i. The formula thus becomes 

JF=-1 DK 2 . • . 53). 

i 

If it be inconvenient to take three readings for each ob- 
servation (namely, Z>, e, and z), or if an amperemeter be not 
available, we may use the wattmeter itself as a dynamo- 
meter and plot beforehand a series of readings connecting 
e, £, and R so that R is given by a curve as a function of 
e. We need then only observe D and e and insert the 
value of R taken from the curve. 

If the wattmeter is connected up as shown in Fig. 82 
the power measured by it includes that wasted in the re- 
sistance, that is to say, it measures the total output coming 
from the alternator. To obtain the power given to B we 
must deduct from the measurement taken on the watt- 
meter the power wasted in the resistance e 2 /R. It is, how- 
ever, possible to connect up the instrument in such way 
that only the power given to the coil B is measured. This 
can be done by simply changing the connections between 



WATT METER. 



237 



terminals T L and T 3 when the current for the fixed coil 
will be taken off before the movable coil is reached, so 
that the current in the latter is the same as that passing 
through B. This arrangement has, however, the disad- 
vantage that the direction of current in the two coils is 
opposed, p?*oducing deflection in the contrary sense, for 
which the instrument is as a rule not suitable. To meet 
this difficulty it is necessary to remove the internal con- 
nection df and to arrange the instrument with four ter- 
minals as shown in Fig. 83. By connecting T Y and 7^ the 

Fig. 83. 



,rr 



T 




A^ 




t9 B 

— mm- 



current for the fixed coil does not pass through the mov- 
able coil and the power measured does not include that 
wasted in R. As far as the reading is concerned it is ob- 
viously immaterial whether R is inserted as shown or 
between T x and 7\, but the latter method of connecting 
up the instrument is objectionable because it then has to 
withstand the whole difference of potential between T x and 
T 2 , which on high-pressure circuits may lead to a break- 
down. 



■HMH 



HM 



238 ELECTRIC TRANSMISSION OF ENERGY. 

The wattmeter may also be used to determine the phase 
difference between two currents of the same frequency, or 
if applied as shown in Fig. 82, the lag of current behind 
impressed E.M.F. Let /and i be the two currents, then 
it follows from 51) that 

DK 2 = Iicosp 54). 

Having determined the deflection D when the instrument 
is coupled up as a wattmeter, change the connections so as 
to use it as a dynamometer and measure successively the 
two currents / and i without changing anything else in 
the circuit. Let D Y be the deflection corresponding to the 
current / and Z> 2 , that corresponding to the current i 3 
then 

I=K S /D l 

which inserted with 54 gives — 

D R 1 = K Z S /D 1 D 2 cos<p. 

cos (p— - 55). 

v/ A A 

It will be seen that for the determination of the lag we 
need not even know the dynamometer constant ; all we 
need do is to take the three readings, using the same 
coils each time, but coupled up as a wattmeter when we 
observe Z>, and as a dynamometer when we observe D x and 
D 2 . The above method of measuring lag is due to Mr. 
T. H. Blakesley, and has been called by him the " Split 
Dynamometer Method." 

When investigating the wattmeter we have assumed 
that it has no self-induction, that is to say, we have 
assumed that the current through the fixed coil is in 



CORRECTION FOR W ATT METER. 239 

phase with the E.M.F. This condition is of course never 
absolutely fulfilled. A circuit arranged to produce 
electro dynamic effects, i.e., mechanical forces, must 
necessarily have self-induction. It is of course possible 
to reduce the effect of self-induction by making the 
resistance R large, but then we also decrease the force 
tending to deflect the movable coil, and therefore the 
sensibility of the instrument. Let us then see what the 
effect of self-induction will be. In the first place it will 
produce a lag of the current i behind the E.M.F. e. Let 
this lag be ^, and let, as before, <p be the lag of /behind e. 
If I is the coefficient of self-induction of the fixed coil 
then 

, 2 7T ~ 7 

tan ^ = — — =— . 
Jti 

Similarly, if L is the coefficient of self-induction in the 
main circuit of which the movable coil forms a part, 

2 7T ~ L 

tan <p = , 

r 

r being the equivalent resistance of i?, as before explained. 
Let in Fig. 84 O E represent the impressed effective 
volts, and O /the effective current, then projecting E 
on Olwe get the point E 1 , O E 1 being the component 
of E.M.F. in phase with the current. The true power 
in watts is therefore O Ix O E l , whilst the apparent 
power given by the wattmeter is O I x O E . The 
point E is the projection of E 2 on O i", and E 2 is the pro- 
jection of E on the line representing z, which makes with 
e the angle ^. To get true watts from the reading we 
must therefore multiply the latter by the ratio 

O E l O E cos <p 

O E = O E cos ^ cos (P—+) 



240 



ELECTRIC TRANSMISSION OF ENERGY. 



If w be the true and w l the apparent watts we have 
therefore 



iv = w 



cos <p 



cos 4' cos (<p— 40 



56) 



The angle 4/ being a constant appertaining to the instru- 
ment can be determined once for all by measuring the 
self-induction of the coil with a secohm-meter, or by 
making a power measurement upon an absolutely induc- 
tionless resistance which has been inserted into the place 

Fig. 84. 




of coil B. The lag of / behind i can be determined from 
55) (only that in this case we do not get <p but <p— 40> so 
that all the data required for the correction are known. 
Formula 56) can also be written afc follows": 



w = w 



1 + tan 2 4* 
1 + tan 4 tan <p? 



from which it will be seen that there are two special 
cases where no correction is required. The first case 
occurs if we have a wattmeter so delicately made that a 



CORRECTIONS FOR WATT METER. 241 

sensible deflection is obtained with a very large R. In 
such an instrument the effect of self-induction will be so 
small that ^ approaches sufficiently close to zero to be 
neglected. In this case the term giving the corrections 
becomes unity. The second special case occurs if the 
self-induction of the fixed coil is equal to that of the 
machine or apparatus under test. In this case tan 2 ^ = 
tan \J/ tan <p, and the term again becomes unity. If ^ < <p 
the wattmeter gives too large a value for the power, and 
if \L > <p it gives too small a value. For ^ > <p there is 

no limit to the error, since for + = - the reading becomes 

zero, and the correction infinite. This case is, however, 
of no practical importance. Modern wattmeters have 
very little self-induction, and the angle ^ is therefore 
always small and generally smaller than (p. It has been 
shown that no correction is required for 4^ = and^ = <p ; 
between these limits there is a value of ^, for which the 
correction becomes a maximum. This occurs obviously 
when the point E\ in Fig. 82 is farthest from 15 a position 
which is reached when the line E E\ forms a tangent to 
the semicircle that can be drawn over O E as diameter. 

It will be easily seen that in this case ^ = -. If, then, 

we have a good instrument in which ^ is under all cir- 
cumstances small and certainly smaller than <p, then the 
greatest possible error due to neglecting the correction 

will be by formula 56) cos (p/cos 2 -. The error may be 

less, but it cannot be more. The following table shows 
the maximum value of the correcting factor for various 
angles of lag, and also the maximum possible percentage 
error if the corrections be neglected : 

R 



242 ELECTRIC TRANSMISSION OF ENERGY. 



ngle of 


Apparent 


True 


Percentage 


Lag. 


Watts. 


Watts. 


Error. 


5° 


1000 


998-5 


•15 


10° 


1000 


994-6 


•54 


15° 


1000 


9827 


1-73 


20° 


1000 


968-8 


3-12 


25° 


1000 


950-8 


4-92 


30° 


1000 


928-2 


7-18 



CHAPTER VIII. 

Self-induction in Armature — Effect of Armature Reaction on the Field — 
Best Frequency — Transmission of Power between two Alternators — 
Margin of Power — Influence of Capacity." 

In the foregoing chapter it has been shown how self- 
induction in the current-receiving circuit produces a lag 
of current behind the impressed E.M.F. TVe have 
simply assumed that a given E.M.F. is applied by the 
alternator to the terminals of the circuit, but we have not 
investigated the relations between this E.M.F. and that 
generated in the armature of the alternator. This we 
now proceed to do. It has already been shown how the 
E.M.F. generated in the coils of the armature can be 
calculated, and it is obvious than on open circuit the 
terminal E.M.F. must be the same as that generated. 
It will also be readily understood that by varying the 
exciting current we can vary the E.M.F., and that the 
relation between these two quantities may be represented 
by a curve which (analogous to that of continuous cur- 
rent machines) we may call the static E.M.F. charac- 
teristic of the alternator. If the external circuit of the 
machine be now closed and a current be allowed to flow, 
we obtain a lower E.M.F. at the terminals, the reduction 
being due to three causes: (1) Armature resistance, 
(2) Self-induction, (3) Armature reaction. As regards 
the loss of E.M.F. by reason of the armature resistance, 
this is of course easily calculable by Ohm's law and need 



244 ELECTRIC TRANSMISSION OF ENERGY. 

not be further considered. In phase this E.M.F. coin- 
cides of course with the current. The E.M.F. of self- 
induction is not so easily determined. It is due to the 
fact that the current passing through the armature coils 
creates a fields the lines of which encircle the conductors 
precisely in the same way as we found to be the case 
with coil B, Fig. 77. This E.M.F. lags behind the cur- 
rent by a quarter cycle ; and in order that the current 
may flow, there must be acting a precisely equal and 
opposite E.M.F. This must obviously be a component 
of the total E.M.F. generated in the armature, and must 
lead before the current by a quarter cycle. If the 
co-efficient of self-induction were constant and a known 
quantity, this component could also easily be calculated 
beforehand. 

The total strength of the self-induced armature field 
must necessarily depend on the relative position of arma- 
ture coils and field magnet poles, and as this is constantly 
changing, the co-efficient of self-induction must also 
change. It must also depend on the excitation of the 
field magnets, because with a strong main field, when 
the magnets already carry a large flux, they are less 
permeable to additional lines of force. The limits within 
which this change takes place are however not very wide. 
Professor Ayrton, when testing a Mordey alternator by 
means of a secohm-meter, found that with a non-excited 
field the self-induction varied between *036 and '038 
henry, and that both values decreased by about 14 per 
cent, when the field was excited. 

It would thus seem that for constant excitation we 
may without serious error assume the self-induction to 
be the same for all positions of the armature, and calcu- 
late the E.M.F. required to balance it by formula 42). 



SEL F-IND UCTION. 



245 



The E.M.F. induced in the armature coils may now be 
considered the resultant of three different components. 
First we have the terminal E.M.F. which does useful 
work and will be in phase with the current if the ex- 
ternal circuit contains no self-induction, and will lead 
before the current if it contains self-induction. Next we 
have the E.M.F. due to ohmic resistance in the armature 
which is in phase with the current, and, thirdly, we have 
the E.M.F. necessary to balance that produced by self- 
induction which leads in front of the current by a quarter 

Fig. 85. 

F 




cycle. These relations are shown in the clock diagram, 
Fig. 85, where OA measured along the current line 
represents the E.M.F. doing useful work in the external 
circuit, A B the E.M.F. of self-induction in the external 
circuit, B C the loss due to ohmic resistance in the 
armature, and C E the E.M.F. of self-induction in the 
armature. The length of the lines AB, B C, and C E 
being proportional to the current, it follows, that if we 
wish to vary the current and at the same time keep the 
useful E,M.F. OA constant (the usual condition for 



246 ELECTRIC TRANSMISSION OF ENERGY. 

lighting and motor work), the point E must remain on 
the straight line A D. For larger currents, E will shift 
further up, and O E must be made larger by increasing 
the excitation ; for smaller currents, E will shift down- 
wards, and O E must be made smaller by decreasing the 
excitation. If provision be not made for altering the 
excitation in this manner, the useful voltage will vary. 
The extent of this variation can be seen from the diagram. 
If O A represents the useful E.M.F. at full load and the 
load be diminished without altering the excitation until 
it is zero, the point E will come down on the circle to E , 
and the useful E.M.F. will go up in the ratio O A to 
OE . 

The diagram also shows what will happen if the machine 
be short circuited at the terminals. In this case the 
external self-induction is cut out and the induced E.M.F. 
is the resultant of only two components, namely, those 
due to resistance and self-induction in the armature. If 
we draw a line from O parallel to B E, we obtain O F 
as the new position of induced E.M.F. The triangles 
O G F and B CE are similar, and since C E is propor- 
tional to the current at full load (and may by a suitable 
choice of scale be made to represent the current), G F 
measured with the same scale will represent the current 
on short circuit. In other words, the current on short 
circuit will exceed ordinary full load current in the ratio 
of CE to G F. This is, however, only an approximation. 
In reality, the current on short circuit will be smaller, 
owing to the weakening of the field on account of arma- 
ture reaction as explained below. For the safety of the 
machine it is of course desirable that the increase of cur- 
rent on short circuit should not be too large so that the 
armature may not be overheated, There is when a 



SELF-INDUCTION, 247 

short circuit occurs also the danger of racing. In a con- 
tinuous current machine a short circuit will most likely 
pull up the engine, but in an alternator it takes the load 
off, and allows the engine to race unless otherwise 
governed. It will be shown presently that power may 
be transmitted by two alternators, one acting as gene- 
rator and the other as motor, the latter running under 
normal conditions synchronously with the former, but 
that under excess loads the motor may fall out of step 
and come to rest. In such an event the circuit would 
be deprived of the counter E.M.F. in phase with the cur- 
rent, and there would be only the resistance of line and 
machines and the self-induction of the latter to limit the 
current. It is thus evident that if we wish to provide for 
the safety of the plant in the event of the motor being 
forcibly stopped, the machines must be so designed as to 
have an appreciable self-induction. On the other hand, 
large self-induction, as will be shown presently, tends to 
reduce the total power of the motor, and this may bring 
about the very evil which it is intended to cure. For 
the generator too large a self-induction is objectionable 
for two reasons ; first, because the power given out by 
the machine is sensibly less than corresponds to the 
product of amperes and volts (the power being propor- 
tional to the cosine of the angle of lag), and, secondly, 
because the excitation must be regulated within wider 
limits in order to keep the useful voltage constant. The 
latter defect is especially objectionable if the current is 
required not only for power, but also for lighting, because 
it entails more supervision at the central station. We 
see thus that safety and convenience in working alter- 
nating current plant are to a certain extent contradictory 
requirements. The best design is necessarily a compro- 



248 ELECTRIC TRANS3IISSI0N OF ENERGY, 

mise, and no hard and fast rules applicable to all cases 
can be given. It may, however, be said that modern 
alternators by the best makers are designed so as to have 
an E.M.F. of self-induction (C JE in Fig. 85) not less 
than 20 or more than 40 per cent, of the terminal E.M.F. 
In the beginning of this chapter it was stated that 
there are three causes tending to lower the E.M.F. of an 
alternator. Two of these we have considered above. 
The third, namely the reaction of the armature current 
on the field-magnets, must now claim our attention. It 
will be obvious that if there is no lag or lead of current 
as compared with the induced E.M.F. the general effect 
of the armature current on the field-magnets must be 
zero ; because everything being symmetrical, the mag- 
netizing action of the current in a group of wires whilst 
approaching the centre of the pole piece is precisely 
balanced by the demagnetizing action when receding 
from the centre. If, however, there is lag or lead of 
current, this symmetry is disturbed and one action pre- 
ponderates over the other, with the result that the field is 
either weakened or strengthened. The effect is different 
accordingly as the machine is used as a generator or as a 
motor, as will be readily seen by reference to the following 
diagrams. Let, in Fig. 86, iV, S represent the radial 
magnet poles of an alternator with drum wound armature. 
For convenience of illustration, the poles are shown in a 
straight line, so that the part of the armature A under 
consideration would have a rectilinear instead of a rotary 
movement. Say the movement is from left to right as 
indicated by the arrow, and let the machine work as a 
generator. The shaded rectangles B, C, D represent the 
cross section through groups of wires belonging to the 
different armature coils. How the wires in each group 



ARMATURE REACTIOX. 



249 



and the coils are joined up is immaterial to our investiga- 
tion, provided the connections are so made that the cur- 
rent in all the wires of one group flows in the same way, 
and the current in all the wires in the next group flows 
the opposite way, this being obviously the only correct 
method of winding. The combined effect of the currents 
in the single wires is then equivalent to that of a broad 
sheet of current flowing alternately towards and from the 
observer within the winding spaces B, C, Z), etc., as indi- 
cated by the little circles with dots and crosses placed 
under each group of wires. Supposing the current lags, 
then it will attain its maximum value after the centre of 

Fig. 86. 



N 




S 




N 




S 



V/////////A 


BWSSS 


V/////////A 


f\\\W^ 


®B 


©c 


©D 

> A 









> A 





each group has passed the centre of the pole piece, and 
the armature at that instant will occupy the position 
shown in the diagram. In that position all the wires 
beyond the edge of the pole piece will obviously exert a 
demagnetizing influence on the field, and this influence, 
as far as it is determined by position, will increase as 
more and more wires emerge ; though as far as deter- 
mined by current strength it will decrease, because the 
current decreases from that moment. If the current 
passes through zero before all the wires have passed 
under the edge of the succeeding pole piece there will be 
excited a magnetizing action tending to strengthen the 
field, but owing to want of symmetry brought about by 



250 



ELECTRIC TRANSMISSION OF ENERGY. 



the lag of current behind the E.M.F., this magnetizing 
action is weaker than the previous demagnetizing action, 
and the net result is that the field is weakened by the 
armature current. If, on the other hand, the current 
leads, and if we again draw the armature in the position 
it occupies when the current is a maximum, we see from 
Fig. 87 that the magnetizing action is stronger than the 
demagnetizing action, and that the armature current 
will now strengthen the field. 

Since in a machine working as motor the current is 
reversed, these actions will also be reversed, and we find 
thus the following rules : 

Fig. 87. 





N 




S 




N 




5 






















f?2%? 


ks^s 


V/////, 


tss^ 


®_B 


©c 




®D 
A 


© 



















A lagging current weakens field of generator. 

A lagging current strengthens field of motor. 

A leading current strengthens field of generator. 

A leading current weakens field of motor. 

The exciting power in ampere-turns by which the field 
excitation is altered in consequence of the armature 
current may be approximately calculated by the formula 

^ = •0156 a i <p° 57), 

if w denotes the number of wires in one group, i the 
effective current through one of these wires, and <p° the 
angle of lead or lag in degrees. 

We have already seen that the self-induction of the 
armature causes a reduction of terminal E.M.F. at load ; 



ARMATURE REACTION. 251 

it also causes lag, and consequently weakening of the 
field, which again reduces the induced and consequently 
also the terminal E.M.F. There is thus a kind of 
cumulative action going on which produces a greater 
drop in terminal voltage at load than corresponds to 
self-induction alone, and at short circuit the current will 
be less than determined from diagram, Fig. 85. Since 
on short circuit <p° becomes nearly 90°, the demagne- 
tizing ampere-turns produced by the armature are 1*4 oo z, 
and i need not be so very large to produce a very material 
reduction in the field strength. 

Before discussing the question of the transmission of 
power by means of alternators, it will be useful to briefly 
investigate the effect of armature reaction and self- 
induction on the general design of such a machine, espe- 
cially as regards the frequency to be adopted. Taking 
lighting and power purposes together we find that in 
respect of this point the greatest diversity prevails in 
practice. In the United States the frequency most 
customary is 133 complete cycles per second, though a 
lower frequency is occasionally adopted, especially in 
more modern designs. In Great Britain the frequency 
adopted by various makers ranges from 100 to 75, and 
on the Continent from 65 to 44 or thereabouts. In the 
case of the Niagara power transmission the frequency 
adopted by the maker of the first instalment of the plant 
is only 25, whilst even a lower frequency had been 
originally suggested by the consulting electrician to the 
company. When we thus see that in practical work 
there is so much discrepancy on the question of fre- 
quency, it is obvious that no hard and fast rule applicable 
to all cases can be given, and that each case must be 
judged on its merits. Thus the method of driving and 



252 ELECTRIC TRANSMISSION OF ENERGY. 

the speed of the machine, its type, permissible weight, 
and many other considerations must influence the choice 
of frequency. As the question is far too complicated 
to be discussed in its most general aspect, it will be best 
to leave out of consideration all matters which may be 
considered as of purely local importance, and to limit the 
investigation to the weight and cost of the machine and 
its working, as far as these points are influenced by the 
frequency. 

Let us assume that we have to compare two machines, 
both designed for the same voltage, speed, and output ; 
but let the frequency of the first machine, A, be twice 
as great as that of the second machine, B. Thus A may 
have 20 poles, and run at 540 revs., giving ~ = 90, whilst 
B has only 10 poles, giving at the same speed ~=45. 
Since the voltage is proportional to r z p, it is obvious 
that t z in B must be twice as great as in A. Let us 
at first assume that B shall have the same weight as A, 
then z in B may be twice as great as in A, and t will 
be the same in both. Each armature coil in B will have 
twice as many turns as in A, and since the coil, taken as 
a whole, is larger (owing to twice the induction having 
to pass through it), the total length of wire in the arma- 
ture of B will be larger than in A. On the other hand, 
the diameter of the armature of B can be made smaller, 
because less space is lost in the gaps between adjacent 
poles, there being only 10 gaps in B as against 20 in 
A. The gaps in A cannot be made too small, as other- 
wise the magnetic leakage would be too large. Further, 
as there are in B only half as many field-magnet cores 
to excite as in A, the excitation in B will, notwith- 
standing the greater bulk of each of its magnets, require 
less wire and less exciting energy than that in A. Thus 



BEST FREQUENCY. 253 

far the balance of advantages lies rather with the machine 
of lower frequency. Let us now see how the case stands 
with regard to self-induction and armature reaction. 
The self-induced field of an armature coil may approxi- 
mately be considered proportional to the armature cur- 
rent, the number of turns of wire in the coil, and the 
dimensions of the latter. The current is the same in 
both machines, but each coil of B has twice as many 
turns as each coil of A, and has also twice the area. 
The self-induced field in B will therefore be four times 
as great as in A. This field cuts the wires of the coil B 
with a frequency of 45, whilst the corresponding field in 
A cuts its wires with a frequency of 90. The product 
~ u (frequency and turns of wire in one armature coil) 
being necessarily the same in both machines, it follows 
that the E.M.F. of self-induction in one armature coil of 
B is four times as great as in one armature coil of A, 
but since A contains twice as many coils as B, the 
E.M.F. of self-induction of the whole armature of B is 
twice as great as that of the whole armature of A. If 
the lag of current were the same in both armatures, the 
armature reaction on the field would be twice as great in 
B as in A, but if the machines both work as generators 
the lag of B would (owing to greater self-induction) be 
greater than in A, and consequently the armature re- 
action would be more than twice as great. The net 
result of all this will be that the E.M.F. characteristic 
of A will drop less than that of B. 

If we wish to get as small a drop in B as in A we 
must reduce its E.M.F. of self-induction and its armature 
reaction. This may be done by increasing z and re- 
ducing t, and also by increasing the resistance of the 
magnetic circuit, so as to reduce the self-induced field. 



254 ELECTRIC TRANSMISSION OF ENERGY. 

The first remedy leads of course to an increase in weight, 
and the second to an increase in the exciting power 
required, because greater magnetic resistance means 
more copper in the field and more exciting energy. 
Thus, although a low frequency tends to make the 
machine less costly, because there are fewer parts, and 
the diameter of the armature may be reduced as com- 
pared with a high frequency machine, these advantages 
may be lost again by reason of the extra weight of field 
required to provide against the effects of greater self- 
induction and armature reaction. To sum up : 

A machine for high frequency and one having a large 
number of field poles must be of large linear dimensions, 
and must be costly on account of multiplicity of parts, 
though it need not be heavy. Its characteristic has a 
small drop. 

A machine for low frequency, and one having a small 
number of field poles, is more compact, but also heavier. 
Its characteristic has a larger drop. 

In determining the frequency there are, however, also 
other considerations which must be taken into account. 
Thus, if the current is required partly for power and 
partly for light, the frequency should not be less than 
about 42 cycles per second, because at a lower frequency 
alternating current arc lamps work badly. On the other 
hand, a high frequency may become objectionable on 
account of the capacity of the line, especially if the latter 
is long and consists of concentric cable laid underground 
and the voltage is high. Under these conditions the 
line absorbs current by virtue of its electrostatic capacity, 
and this current leads by a quarter period over the 
E.M.F. This current is, of course, directly proportional 
to the frequency, and as owing to its lead of 90° it 



BEST FREQUENCY. 255 

carries no power, whilst wasting power by heating the 
conductors in circuit, it is desirable to keep it as small 
as possible. Hence if the line has great capacity the 
frequency should be low. As regards small motors a 
low frequency is also desirable. It will be shown later 
on that all motors, whether single or multiphase, run very 
nearly at a speed directly proportional to the frequency 
of the supply current and inversely proportional to the 
number of poles in the field. To get a moderate speed 
we must therefore either have a low frequency or build 
motors with many poles. The latter expedient is easily 
adopted in large motors, but not so easily in small ones ; 
hence where the subdivision of power between many 
small consumers is of importance, the frequency adopted 
should not be too high. Taking these various require- 
ments together we find that the right frequency for power 
lines is a compromise, and practical experience goes to 
show that in the majority of cases a frequency between 
40 and 65 is the best. 

After this digression we can now return to the problem 
of power transmission by alternating current. We take, 
as the simplest case, the transmission of power between 
two similar single phase alternators by means of a 
perfectly insulated line having only resistance, but no 
self-induction and no capacity. The last two conditions 
are very nearly realized in practice with aerial lines of 
moderate length. We shall also, for the sake of sim- 
plicity, assume that the armature reaction, both in the 
generating and receiving machine, is negligible, and that 
the self-inductions in them are constant and known 
quantities. Assume that both machines are running at 
the same frequency, and that the excitation of the two 
fields is so adjusted as to produce E x volts in the genera- 



256 ELECTRIC TRANS3IISSI0N OF ENERGY. 

tor and E^ volts in the motor. Let the total resistance 
in circuit (that is, the resistance of the two armatures and 
line) be r ohms, and- let the current be i amperes. If L Y 
be the co-efficient of self-induction in the generator, and 
L 2 that in the motor, the E.M.F. of self-induction is 
respectively 

e sl = 2 m ~ L x I 

e s2 = 2 w ~ L % i> 

or, taking the two machines together, 

«,= 2»- (A + A) u 
The loss of pressure by resistance is 



We can now construct a clock diagram to show the 
working of the plant. In drawing such a diagram we 
may start by fixing the instantaneous position of any one 
quantity, and build up the whole diagram to suit the 
first assumption. In the present case it is most simple 
to start with the current. Thus, let in Fig. 88 01 
represent the current line taken at the moment when the 
current passes through zero, and O R the voltage lost by 
resistance. From what has been said in the beginning 
of this chapter, it will be clear that the E.M.F. required 
to overcome self-induction must be in advance of the 
current by a quarter period, that is to to say, the radius 
representing e s must at this moment point vertically up- 
wards. Since we know e s from above formula, we can 
draw its radius in the diagram. Let this be O S. We 
know now that the two machines must combine in such 
way as to produce in the circuit simultaneously the 
E.M.F. e r = O R and the E.M.F. e s = O S\ that is to 
say, they must produce the resultant c = O A ; because 



CLOCK DIAGRAM FOR POWER. 



257 



only if this condition is fulfilled can the current 01 flow. 
It is important to note that the direction of this resultant 
is independent of the strength of the current. It is given 
by the tangent of the angle A O I, and its expression is 

t*n A OI= 2 *~ C^ + A) 



Let the circles 1 and 2 be drawn with radii representing 

Fig. 88. 




the E.M.F. of generator and motor respectively. The pro- 
blem is now to find the position of these radii corresponding 
to the the position of the current line originally fixed. We 
know that O A must be the resultant of the two E.M.F.'s, 
and we have therefore to find what parallelogram of 
forces, having E x and E 2 for sides, will give O A as the 
resultant. It is clear that only two such parallelograms 
are possible, one being shown in Fig. 88, and the other 
ip Fig. 89. In the former figure O E x lies on the same 

s 



258 



ELECTRIC TRANSMISSION OF ENERGY. 



side as O i, and this means that the machine gives power 
to the current, that is, acts as a generator. The E.M.F. 
line of the other machine lies on the opposite side to O /, 
that is to say, the current passes through the armature 
in opposition to its E.M.F., and therefore does work on 
the machine, which acts as motor. Since in the diagram 
JE X is shown larger than K z , we find that the stronger 
machine is the generator, and the weaker machine is the 
motor. The position may, however, also be reversed, as 

Fig. 89. 




shown in Fig. 89. Here the E.M.F. of machine No. 2 
lies on the same side as the current, whilst that of machine 
No. 1 lies on the opposite side. Hence the weaker 
machine is the generator, and the stronger machine is 
the motor. In this respect the transmission of power by 
alternating current differs radically from that by con- 
tinuous current. In the latter the motor must under all 
circumstances have a lower E.M.F. than the generator, 
but with alternating currents the machine of lower voi~ 



CLOCK DIAGRAM FOR POWER. 259 

tage may work as generator and drive the machine of 
higher voltage as a motor. 

The power given to the motor in Fig. 88 is the product 
ofOB volts (this being the projection of O E 2 on the 
current line) and i amperes. Similarly the power given 
by the generator to the line is the product ofOFx i. 
For i we may substitute e s /2 tt ~ (L Y -f- L 2 ) and we thus 
find that the area of the shaded rectangle O S C B is 
proportional to the power given to the motor, and the 
area of O S D F is proportional to the power given out 
by the generator, whilst the area of O SAB is propor- 
tional to the power lost in resistance. To get the exact 
value of any of these powers we measure the rectangles 
by means of the volt scale which was used in drawing the 
diagram, and divide the area by 2 tt ~ {L x + L 2 ) ; the 
power is then obtained in watts. 

The diagram may also be used to show what will 
happen if the load on the motor is kept constant, whilst 
its excitation, and therefore its E.M.F., is raised. Since 
the area of O S C B is to remain constant, the point C 
must lie on a rectangular hyperbola, and its position will 
depend on the E.M.F. of the motor, the E.M.F. of the 
generator being supposed to remain unaltered. Fig. 90 
is drawn to scale for E x = 1000 l r = 1 ~ = 50 L x -\- L 2 
= •0127 2*r~ (Z 1 +Z a )=4 <?,=4 i e r =l i W 2 = 
100,000 watts delivered to motor. The power delivered 
fixes the position of the hyperbola, and we have now to 
find the relation between the E.M.F. of the motor and 
the current for this power. The direction of O a is fixed 
by the condition that the E.M.F. of self-induction is four 
times that required to overcome resistance. If we now 

1 800 volts to the inch. 



260 



ELECTRIC TRANSMISSION OF ENERGY. 



select a point C on the hyperbola, we know that the end 
of the E.M.F. radius of the motor must lie somewhere on 
a vertical line through (7, and we also know that the end 
of the radius giving the resultant E.M.F. must lie some- 
where on a horizontal line through C. It must also lie 
on the inclined line Oct, and we find thus the points by 

Fig. 90. 




the intersection of the two lines. O A is the resultant 
E.M.F. If now with a radius corresponding to 1,000 
volts, and from A as a centre we intersect the vertical 
line through (7, we find the two points G and H, which 
are the ends of the radii representing E.M.F. of motor. 
It will be seen that the same current may be obtained 



CONDITION OF MINIMUM CURRENT. 261 

with two E.M.F.'s of motor, which in this case are 
widely different, namely 680 and 1,370 volts. If we had 
selected the point C higher up on the hyperbola, there 
would have been still greater difference between the two 
voltages at which the motor requires the same current to 
give 100 Kwt. The current is given by the piece cut off on 
the vertical O y by the horizontal line C A. In order to 
waste a minimum of power in heating the resistance of 
the circuit we must so excite the motor as to make this 
current a minimum. We must, therefore, endeavour to 
bring C down to the lowest possible point on the hyper- 
bola. This point is obviously that at which a line drawn 
from K parallel to Oa intersects the hyperbola at E 2 . 
The corresponding point on the line of resultant E.M.F. 
is A 1 , and the voltage of the motor is O E 2 (in this case 
very nearly 1^000 volts). If the motor is excited to give 
the E.M.F. O E Y the line current is a minimum, and 
therefore the efficiency of transmission a maximum. The 
E.M.F. of the generator coincides with the current, and 
the output of the generator is correctly represented by 
the product of current and E.M.F. It is convenient to 
represent the relation between motor voltage and work- 
ing current for constant load also in the way shown in 
Fig. 91. This diagram is obtained from Fig. 90 by 
plotting the voltage of the motor, such as O G, on the 
horizontal, and the corresponding current on the vertical. 
The curve resulting shows at a glance how the current 
varies when the motor voltage is altered. It will be 
seen that, generally speaking, the same current will 
result for two different values of the motor E.M.F., the 
lower value giving a small, and the higher value a large 
lead of current over the E.M.F. It has already been 
shown that a leading current weakens the field of the 



262 



ELECTRIC TRANSMISSION OF ENERGY. 



motor, and this effect is the more noticeable the greater 
the lead. It follows that with a motor too strongly 
excited armature reaction has rather a beneficial effect 
as it in part corrects the error of excessive excitation, 
whilst with a motor too weakly excited the reverse may 
be the case. On account of safety and efficiency it is 
therefore better to work the motor at a voltage rather 
above than below that which, according to Fig. 91, is 



Fig. 91. 













300 

/ 


/ 
/ 

/ 




t 


K 


/ ■"— ■ 








200 y 
















iT 




100 






















10 


00 


20 


00 



theoretically the best. It will be seen from the curve 
that as we reduce the excitation beyond the theoretically 
best point the current increases until we reach a par- 
ticular value when the vertical just touches, but does not 
cut, the curve. This is a critical point. If the excitation 
be still further reduced the ordinate will miss the curve 
altogether, and this shows that the motor cannot work in 
this condition. It must fall out of step and come to rest. 
The same will happen if, working near the critical point, 



MARGIN OF POWER. 263 

the load on the motor should be accidentally increased. 
There is no such critical point to the right of the ordinate 
corresponding to the best point of working, and in order 
to have some margin, both as regards an error in adjust- 
ing the exciting current and an accidental overload of 
the motor, it is best to aim at working it at an excitation 
slightly higher than that which would theoretically be 
best. 

The question of what amount of overload a motor can 
support without falling out of step is a very important 
one. In practical work we cannot expect to know to a 
fraction the exact limit of load which a motor may have 
at one time or another to support. If, for example, 100 
horse-power is under average conditions sufficient to 
drive a factory, it is conceivable that for short periods, 
whilst a heavy tool is set in motion, this limit may be 
considerably exceeded ; and as it would be exceedingly 
inconvenient to have the motor fall out of step and come 
to rest on some such occasion it is important, when de- 
signing the plant, to make provision for a certain amount 
of spare power. The problem may be stated thus : 
Assuming that the engine or turbine which drives the 
generator is so governed as to be able to furnish for a 
short time any excess of power which may be required, 
what is the maximum amount of power that the generator 
can take up and the motor give out without breaking 
down ? We know that with continuous current machines 
this maximum exceeds by many times the normal power, 
and we must now investigate how alternating current 
machines behave in this respect. 

For this purpose we may take as an example the 
machines to which Figs. 90 and 91 refer. Say that the 
normal power required for driving the factory is 125 



264 ELECTRIC TRANSMISSION OF ENERGY. 

horse-power or 93 Kwt. Allowing 7 Kwt. as an outside 
margin for exciting the motor and for its own frictional 
eddy current and hysteresis losses (armature resistance 
being already included in r), then the normal power 
brought to the motor by the supply current will be 100 
Kwt. If the demand for power be reduced to zero, then 
the supply current will have to bring in merely the 
7 Kwt. required to cover the various losses, and if the 
demand for power be increased beyond 125 horse-power, 
then the supply current will have to bring in a cor- 
responding excess over the normal 100 Kwt. until a 
point is reached when the available margin of power in 
the motor is exhausted and the system breaks down 
altogether. 

We neglect again armature reaction and capacity of 
line ; and assume that the total resistance in circuit is 
one ohm whilst the total self-induction in circuit is such 
as to give at 50 cycles per second e s = 4:i. If the trans- 
mission were by continuous current, the 100 Kwt. would 
be delivered at the motor end by a current of 100 a and 
1,000^., and if the efficiency of transmission is to be 90 per 
cent., this would require a pressure of 1,100 volts at the 
generator end. We shall, therefore, assume that the 
alternator at the generator end is excited so as to give 
this effective E.M.F., and then the motor in order to 
work with a minimum current would have to be excited 
so as to give a slightly lower pressure (see Fig. 90), but 
in order to have a margin of safety, as explained a few 
pages back, we will excite the motor so as to give a some- 
what higher E.M.F., say 1,150 volts. It may here be 
explained that the voltage of the plant has been chosen 
low merely for the convenience of obtaining a better 
scale for the diagrams. In practice there is no difficulty 



CURRENT AT SHORT CIRCUIT. 265 

whatever in using an E.M.F. up to 5,000 volts, and even 
higher, without transformers if the distance of transmission 
is considerable. 

We have then the following data on which to construct 
the working diagram of the plant 

^=1,100 .# 2 =1 ? 150 e r =l.i e s = 4.i r=l —=50 
(i 1 + ^ 2 ) = '0127 e = 4-123t i='242e. 

In the first place we must ascertain whether in the 
event of the motor coming to rest through being over- 
loaded, the current will remain within safe limits. As 
with the motor at rest JZ 2 = the whole E.M.F. of the 
generator (in this case 1,100 volts) will be used up in 
overcoming the resistance and self-induction of the 
circuit. The E.M.F. of the generator will, therefore, be 
the resultant E.M.F. or e = 1,100 if, as stated above, 
we neglect armature reaction for the present. We 
find that under these conditions the current will be 
•242 x 1,100 = 266 amperes, or about 2\ times the normal 
working current. Whether this current will injure the 
armatures by overheating depends on their resistance. 
The total resistance in circuit is 1 ohm, and the total 
power absorbed will, therefore, be only 71 Kwt., which 
is less, than the power given out by the motor under 
normal working conditions. Of that power the greater 
part is of course absorbed in the line. The remainder is 
absorbed in heating the two armatures. Now the re- 
sistance of armature in modern machines is very low. 
There is no difficulty in designing alternators so that the 
loss of pressure due to armature resistance shall not 
exceed 2 per cent., and even 1 per cent, is a perfectly 
feasible limit. In the machines with which we are deal- 
ing and which are of the author's type, specially designed 



266 ELECTRIC TRANS3IISSI0N OF ENERGY. 

for power transmission, the loss is about \\ per cent, at 
full load. Thus, with 100 amperes flowing, the loss 
would be about 14 volts in each armature and with 266 
amperes, it would be 37 volts, that is under 3^ per cent, 
of the terminal voltage. The corresponding power is 
under 10 Kwt. for each armature, which is so small an 
amount of power that we need not fear any damage to 
the armatures by overheating. It will be shown later 
on that even this moderate limit cannot be reached in 
practice provided the generator is properly designed so 
as to take advantage of armature reaction, but for the 
present we may rest satisfied that the plant will be safe 
against overheating under all conditions. Whether it 
will be safe against mechanical stresses is another question. 
Although the power given to the line by the generator 
in the event of the motor being forcibly stopped is only 
71 Kwt., the mechanical stresses between the field poles 
and armature coils in the generator are much greater 
than corresponds to the output. This may be clearly 
seen from Fig. 92 where oe is the resultant E.M.F. (in 
this case coincident with the E.M.F. E x of the generator) 
and o i the current. As we are now dealing with instan- 
taneous values, these lines must be drawn to represent 
maximum and not effective values. Thus, o e will not 
be 1,100 volts, but </2x 1,100= 1,540 volts, and ozwill 
be \/2x666 = 373 amperes. The mechanical stress on 
the armature coils is at all times proportional to the 
product of instantaneous current and instantaneous 
strength of field, or what comes to the same thing, instan- 
taneous E.M.F. It may, therefore, -be represented to a 
suitable scale by the product of the projections of e and i 
on the vertical ; thus : 

Stress=0^x OB. 



MECHANICAL STRESS AT SHORT CIRCUIT. 



267 



If A and B lie both above 0, the stress is in one 
direction ; if one lies above and the other below 0, it is 
in the other direction, whilst it is zero at any time that 
either e or i changes sign. The question we have to 
investigate is : at what phase during the cycle is the 
product O A x O B a maximum, and what is the relation 
between this maximum and the normal stress when the 
machine is working under full load? In the latter case, 
z = 140, and E= 1,540, and the two may for our present 
purpose be assumed to coincide. The stress will then 



Fig. 92. 



~- -> e 




never change sign, and its maximum will be propor- 
tional to 215,000. When the generator is working on 
short circuit, the lag ^ between e and i is known from 
the relation that e r : e s = 1 : 4, to which corresponds t// = 76°. 
Let the phase for which the diagram is drawn be repre- 
sented by the angle a, then we have to find the relation 
of a and ^ for which the stress becomes a maximum. It 
is obvious that 

O A x O B = ei cos (\J/ —a) cos a, 

and by differentiating to a and equating to zero we find 



268 ELECTRIC TRANS3IISSI0N OF ENERGY. 

2 tn a 



tn$ 



1-tn 2 - 9 



a 



from which a= -, 



The maximum stress will occur when the vertical is 
midway between the volt line and ampere line, that is 
for the phase characterized by a = 36°. The cosine of 
36° is # 809, and the stress at that moment is 

OA x OB = 1,540 x 373 x 654 
= 377,000, 

or about If times as great as when the machine is 
working under normal conditions. There should be no 
difficulty in providing a sufficiently substantial method 
of construction to render this comparatively small in- 
crease in the mechanical stresses perfectly harmless ; and 
having now satisfied ourselves that the plant will be safe 
against overheating and mechanical failure, Ave may 
proceed with our investigation as to its working condition 
when the load on the motor is varied. 

We draw the clock diagram at the moment when the 
E.M.F. of the generator has attained its positive maxi- 
mum, OE x > Fig. 93, and we assume the position of the 
E.M.F. of the motor at E 2 on the 1,150 volt circle. We 
then find the resultant e ; and since the relation between 
e r and e s is given, the angle 0, by which the E.M.F. 
opposed to self-induction leads over the resultant E.M.F. 
is also given (in our case 14°), we can draw the lines 
representing e s and e r . The current line must be at right 
angles to e s9 and can now be drawn in, its length being 
determined from the equation i = '242 e above given. 
To find the power corresponding to the selected position 



WORKING CONDITION OF PLANT. 



269 



of i?2? we prolong E % backwards and project i on it 
(dotted lines). If we measure this projection with the 
ampere scale, and multiply with 1,150, we obtain the 

Fig. 93. 



£?° cK.VH 




ie^j 



power given to the motor in watts. This may be plotted 
to any convenient scale on the radius giving the motor 
E.M.F. We obtain thus the point w 2 . Similarly, if we 
project the current line on the vertical, and multiply the 



270 ELECTRIC TRANSMISSION OF ENERGY. 

scaled amount with 1,100, we obtain the power given out 
by the generator, plotted at co v The difference, cc L —co 2i 
is of course the power lost in resistance, ri 2 , and the 
accuracy with which the diagram is drawn may thus be 
checked. By assuming different positions of JE 2 on the 
1,150 volt circle we can find a succession of points giving 
the corresponding power of motor and generator, which, 
if joined, give the two power curves shown in thick lines. 
It may here be remarked that if the resistance in circuit 
may be neglected these curves coincide and become a 
true circle with its centre in the horizontal axis of the 
diagram. The power curves show very clearly the 
working condition of the plant. If, for instance, the load 
on the motor be such as to require the supply of 100 
Kwt., the E.M.F. line of the motor will assume the 
position OA. If the load be reduced this line will 
advance towards the vertical ; in other words the E.M.F. 
of the motor will come nearer to the point of exact 
opposition to the E.M.F. of the generator. Now suppose 
that the load on the motor is suddenly increased. This 
will to some extent retard the motion and cause the 
armature of the motor to lag, thereby increasing the 
angle between OE % and the vertical. As we see from 
the diagram, this is exactly what is wanted, because it 
brings the armature into a phase where it is capable of 
giving out more mechanical power. In this region of 
the diagram the working is perfectly stable. If the load 
be increased to 200 Kwt,, the E.M.F. radius of the motor 
will assume the position OB. The load may even be 
increased beyond this point, but not very much, for at 
224 Kwt., which corresponds to the position 0(7, we have 
reached the very utmost limit of power, whilst the current 
as given by the line marked u amperes " is very great. 



EFFECT OF ARMATURE REACTION. 271 

and the efficiency very low. At this point the motor 
becomes unstable (dotted part of the power curve). Any 
slight increase of load brings the E.M.F. radius further 
back and diminishes the available power. The motor is 
therefore not able to cope with the increased load, and 
must fall out of step. We see thus that in the example 
chosen, and provided we may neglect armature reaction, 
the load on the motor will have to be more than doubled 
before the system of transmission breaks down. 

But now the question presents itself: are we justified 
in neglecting armature reaction ? This depends on the 
design of the machines, but as a general rule it will be 
found that the armature reaction is too important to be 
neglected. The reason is, that in order to provide for 
the safety of the plant in the event of the motor stopping, 
we are obliged to so design the machines as to have a 
sensible amount of self-induction ; the number of arma- 
ture conductors must therefore not be reduced too much, 
and this means that the ampere-turns produced by the 
armature current are considerable. By working the 
machines with very strongly excited fields, that is, at a 
point well above the knee of the characteristic curve, we 
are able to diminish the relative importance of the arma- 
ture ampere-turns, but even then we cannot render their 
effect negligible, whilst the use of an abnormally strong 
excitation is objectionable for obvious reasons. 

In order to be able to study the effect of armature 
reaction we must, of course, know the characteristic of 
the machine. This can be predetermined in the same 
manner as already explained in connection with con- 
tinuous current dynamos. Let Fig. 94 represent the 
characteristic of the machines previously considered, the 
ordinates being effective volts induced in the armature 



272 



ELECTRIC TRANS3IISSI0N OF ENERGY. 



at the normal speed of 500 revs, per minute, and the 
abscissae being ampere-turns applied to the field. The 
two machines are alike in every way ; each has 12 poles 
and 288 armature conductors, giving co = 24 and by 
Formula 57) # = '373 i (p° as the armature ampere-turns. 
Let us first see how armature reaction affects the 
generator when the motor is forcibly stopped. We have 
seen that if armature reaction were negligible the current 
would be 266 amperes, and the angle of lag 76°. These 

Fig. 94. 































E. 


■\-sso 
















E. 


= 13TO 


















-w 


oo 
















p , 


= 1 IOO 


y 


y 












IOOO 






/ 




















/ 













y^ 






/ 














9 






/ 
































JQO 




































































































J 


ooo 


10 


ooo 


IJ 


ooo \ 


?o 


000 



Cl/i > V J3 C^L& —fctt t ^X^d 



values inserted into Formula 57) give X— 7,570 ampere- 
turns. From the characteristic Fig. 94 we find that the 
fi eld excitation, which produces 1 , 1 00 volts, is 9,000 ampere- 
turns. The current lagging behind the E.M.F. must 
weaken the field, that is to say, if the current of 266 
amperes w^ere by any means maintained, the effective field 
excitation would be 9,000 — 7,570=1,430 ampere-turns 
and the E.M.F. induced in the armature would only be 
about 200 volts, Since there is,, however, no other means 



EFFECT OF ARMATURE REACTION. 273 

for producing the current than the E.M.F. of the arma- 
ture, it is clear that the reduction of E.M.F. will not be 
so great. We can find the exact working condition by 
a tentative method adopting successively different values 
for the effective E.M.F. between the two extreme limits 
of 200 and 1,100 volts, until we arrive at that value of 
E.M.F. at w r hich the armature current will reduce the 
field excitation by exactly the proper amount. It is not 
necessary to give this operation here in detail ; the result 
is that with a current of 150 amperes, to which corre- 
sponds an E.M.F. of 600 volts, the armature demag- 
netizes the field with 4,250 ampere-turns. The field 
excitation remainingis, therefore, 4,750 ampere-turns, and 
by referring to the characteristic we find that this excita- 
tion will, indeed, produce the 610 volts. When the motor 
is forcibly stopped the current will, therefore, not be 266 
amperes, as found when neglecting armature reaction, 
but only 150 amperes. 

The power given given out by the motor when in 
ordinary working condition can be found by using the 
construction shown in Fig. 93, but corrected by reference 
to the characteristic Fig. 94. It will be found that for a 
small output the current leads in the generator ; for a 
moderate output it may lag or lead in the generator, but 
not by any large amount, for a large output approaching 
the breaking-down point the current in the generator 
lags. As regards the motor the current leads at all 
loads. We thus see that as the load increases the field 
of the generator is at first strengthened and then 
weakened, whilst the field of the motor is weakened 
from the beginning ; and it is the more weakened the 
greater the load becomes. For this reason it is advisable 
to excite the motor to a higher E.M.F. than the gene- 

T 



274 ELECTRIC TRANSMISSION OF ENERGY, 

rator, as already pointed out. If we work the generator 
at or slightly below the knee of the characteristic we 
insure the safety of the plant in the event of a short 
circuit, whilst to insure a margin of power we must work 
the motor well above the knee of the characteristic. 
Let us excite the generator with 9,000 ampere-turns, 
giving an E.M.F. of 1,100 volts. By assuming suc- 
cessively 10,800, 15,000, and 18,500 ampere-turns as the 

Fig. 95. 




excitation of the motor (corresponding to 1,200, 1,300, 
and 1,350 volts), we can for each case construct the 
power curves and see at a glance what margin of power 
we have. The construction must be made as in Fig. 93, 
and corrected by reference to Fig. 94, various values for 
JE X and E 2 being tentatively adopted, until by trial and 
error method we arrive at the true values. The con- 
struction need not be explained at length ; it is quite 



EXAMPLE OF TRANSMISSION PLANT. 



275 



simple, though somewhat tedious. The result is shown 
in Figs. 95, 96, and 97. The curve giving the power 
required by the generator has been omitted in all these 
diagrams, the power curve marked Kwt. referring to the 
motor only. In Fig. 95 the power curve resulting from 
the same construction when armature reaction is ne- 
glected, has been shown in a dotted line. It will be 



Fig. 96. 



3 eK. r 1V. 




noticed that up to about 100 Kwt. (being the normal 
load) the two power curves coincide, but they diverge 
for greater loads, and the breaking-down point is reached 
very much sooner than would be the case if armature 
reaction were absent. The diagram illustrates in a 
striking manner the importance of taking armature re- 
action into account in the design of power transmission 
plant, especially as regards the determination of the 



276 



ELECTRIC TRANSMISSION OF ENERGY. 



margin of load on the motor. In the present case the 
breaking-down load corresponds to a supply of 157 Kwt. 
Since 7 Kwt. is required for excitation and to overcome 
losses in the motor, 150 Kwt. or about 200 horse-power is 
the maximum that can be given off. The normal power 
given off is 125 horse-power, so that the margin of power 
is only 75 horse-power or 60 per cent, over the normal 

Fig. 97. 



j^eoiet). 



i\ i ° ■ ■ ■ ■ i 00 . ■ ■ g ? s\)o£t,. 



50 



9>\i° i i i i i i— ■ 

^lo ioo ao 







output. It would scarcely be safe to rely on a trans- 
mission plant which is only capable of carrying 60 per 
cent, excess load. To increase the margin of safety we 
must excite the motor to a higher degree. Fig. 96 
shows the power curve if the motor is excited with 
15,000 ampere turns, giving an E.M.F. of 1,300 volts. 
The current curve has been added, so that by means of 



MARGIN OF LOAD. 



277 



the scale of amperes the current corresponding to any 
load may be read off on the radius representing the 
phase of E.M.F. of motor at the given load. Thus at 
a load of 125 horse-power corresponding to a supply 
of 100 Kwt. the E.M.F. of motor is in the phase repre- 
sented by the radius O i? 2 , and the current is 103 
amperes. The loss by resistance is 10*6 Kwt. ; losses in 
both machines, 14 Kwt ; total losses, 24'6 Kwt. ; power 
delivered, 93 Kwt. ; power supplied to generator, 117*6 
Kwt. Total efficiency, 93/117*6 = 79 per cent. The 
breaking- down load corresponds to a supply of 193 Kwt. 
to the motor. Deducting the 7 Kwt. for internal losses 
we find that 186 Kwt. or very nearly 250 horse-power 
will be given off by the motor before the system breaks 
down. This is a margin of 100 per cent. 

Should we want a larger margin still we can obtain it 
by exciting the motor to a still higher degree. Fig. 97 
shows the power curve when the motor is excited with 
18,500 ampere-turns giving i?i=1350. In this case the 
breaking down load is 200 Kwt. or 268 horse-power, giving 
a margin of 134 per cent. 

These results are summarized in the following table : 

Table showing Working Condition of Transmission Plant. 
Total Resistance in Circuit 1 ohm. Total Inductance 
4 ohms. 



Generator excited to give 
Motor excited to give 


1,100 
1,200 


1,100 
1,300 


1,100 volts 
1,350 volts 


Normal power given off by 
motor 


125 


125 


125 HP 


Maximum power given off 
by motor 


200 


250 


268 HP 


Margin of excess load causing 
breakdown of the system 


60 


100 


134 per cent. 



278 ELECTRIC TRANSMISSION OF ENERGY. 

A careful study of the diagrams here given for one 
particular example, and the application of the same 
methods of investigation to other cases leads to the 
following general conclusion. 

A high resistance, whether this be in the line or in the 
machines, is objectionable, as it tends to lower the 
efficiency and the margin of excess load. To insure 
reliability in working, and an ample margin of power, 
the total resistance in circuit should be as small as 
possible. This rule applies not only to power transmission 
as such, but also to the circuits connecting two or more 
generators, or two or more motors which work in 
parallel. 

A moderate self-induction and a moderate armature 
reaction are desirable in the generator, because ensuring 
the safety of the machine in case of a short circuit. 

In the motor there should be as little self-induction 
and as little armature reaction as possible. 

If motor and generator are machines of the same size 
and type, the motor should be excited to a higher E.M.F. 
than the generator. It is, however, preferable to give 
the motor fewer armature conductors than the generator. 
In this case its self-induction and armature reaction will 
be lower, and it need not necessarily be worked at a 
higher E.M.F. than the generator, the essential condition 
being that the motor should be worked at a point well 
beyond the knee of its characteristic curve. 

The foregoing investigation was based on the assump- 
tion that the line has only resistance, but no capacity. 
In most cases the capacity of the line is so small that it 
may indeed be neglected. A few miles of overhead line 
properly erected need not have more than a small fraction 
of a microfarad of capacity, and the condenser current 



CAPACITY OF LINE. 279 

flowing in and out of the line is so small in comparison 

with the power current as not to disturb the working of 

the plant. There are, however, cases where the capacity 

of the line cannot be neglected, and these occur when the 

distance of transmission is considerable. We are then 

compelled to work at extra high pressure, and the line 

must necessarily have the more capacity the longer it is. 

Both these circumstances tend to increase the condenser 

current. Cases may also arise where, owing to climatic 

or other conditions, an overhead line is not admissible 

and a concentric cable must be used. Such a cable may 

have a very sensible capacity. Thus the Ferranti main 

between Deptford and London has a capacity of *367 

microfarads per mile, and if such a cable were used for a 

transmission at 10,000 volts over a distance of 20 miles 

and a frequency of 50 cycles per second the condenser 

current would be 23 amperes. 

If K represents the capacity of a condenser connected 

to a source of alternating E.M.F. and i the instantaneous 

current, then the increment of charge flowing into or out 

of the condenser during the time d t, when e changes by 

the amount de is i dt — Kde. If e is a sine function of 

de 
the time theni = K- r - must also be a sine function such 
at 

as z = /sin 2 ?r~t. 

We can, therefore, also write 

I sin 2 7T ~ tdt= Kde. 

The total charge of the condenser corresponds obviously 
to the current flowing in or out during a quarter period 
from e = o to e = E, the maximum value of the E.M.F. 
applied. This charge is/Kde = KE or 



280 ELECTRIC TRANSMISSION OF ENERGY. 



■f- 



KE = i I sin 7T ~t dt 



■r 



T 

4 



KE= — Icos 2?r ~ t 

2 7T ~ 
I 



In this equation both E and /are maximum values, but 
as the effective value of both bears the same proportion, 
the formula holds good also for effective values, and we 
have, therefore, the following formula for the condenser 
current : 

4 = 2 7T ~ e K. 

This is in absolute measure. If we have K in micro- 
farads, i k in effective amperes and e in effective volts the 
formula becomes 

4 = 2 7r~e K10- 6 .... 58). 

For a concentric cable in which the inner conductor has 
a radius of r centimeters, and the outer conductor has an 
inner radius of R centimetres (B—r being the thickness 
of the insulation between the two conductors) the capacity 
may be calculated according to the following formula 
given in Professor Ayrton's " Practical Electricity " and 
other text books : 

K= 7 2 ' 413 * l ]° " 7 - Microfarads 59). 
I being the length of the cable in centimeters and e the 



CAPACITY OF LINE. 281 

specific inductive capacity of the insulating material. 
The value of e varies between 25 and 4 according to the 
nature of this material. Taking 3*3 as an average value 
for insulating materials consisting mainly of some heavy 
hydrocarbon compounds, and inserting the length of the 
cable in miles, we have also 

•129 I 
K= - Microfarads . . 60). 

%io — 

For overhead lines the capacity may be calculated by 
the formula given by Steinmetz, 1 

Ml I 10- 6 

4 log net I — ) 

in which I is the length of line in centimetres, r the radius 
of the wire, and d the distance of the two wires. For con- 
venience in use this formula may be transformed into the 
following expression, 

K-^r «>• 

where K is the capacity in microfarads, I the distance of 
transmission in miles, and the denominator the common 
logarithm of the ratio between the distance and radius of 
wires. Thus, if we have wires of 160 mils diameter placed 
3 feet apart, this ratio is 450, and the capacity of the line 
is '00685 microfarad per mile. 

The effect of capacity on the generator and motor may 
be investigated by means of a clock diagram, in a similar 

1 "Elektrotichnische Zeitschrift," 1893, p. 476. 



282 ELECTRIC TRANSMISSION OF ENERGY. 

way to that adopted when dealing with self-induction, 
except that the capacity current must always be drawn 90 
degrees in front of the E.M.F. which produces it. An 
example may serve to show how the capacity of the line 
influences the working conditions of a transmission plant. 
For this purpose we take a rather long underground line 
working at high pressure, because with short lines at 
moderate pressure the influence of capacity is too 
small to show clearly in the clock diagram. Let us then 
assume that the two machines are connected by a con- 
centric cable 10 miles long, and that the effective pressure 
in the cable is 10,000 volts. Let the power delivered to 
the armature of the motor be 500 Kwt. and the total re- 
sistance of the line 10 ohms. The conductors would have 
an area of *085 sq. in., and the insulation between them a 
thickness of about *4 in. The capacity of the whole line 
would be about 3*2 microfarads. This is distributed 
over the whole length of the line, and to calculate the 
exact distribution of the charge would be a very compli- 
cated operation, because that depends on the potential 
difference between the two conductors, and this varies 
along the cable by reason of its ohmic resistance. The 
variation is, however, small in comparison with the total 
potential difference, as will be seen from the following 
preliminary consideration. The total power transmitted 
is 500 Kwt. at 10,000 volts. If there were no lag and 
no capacity the current would be 50 amperes, and the 
loss of pressure over the whole 10 miles of cable would 
be 500 volts or 5 per cent. As, however,, there will pro- 
bably be some lag, and as there must be some capacity 
current, the total current flowing into the line at the 
generator end must be greater than 50 amperes. How 
much greater we cannot yet tell with certainty, but we 



CAPACITY OF LINE. 283 

can make a rough approximation. Let the frequency be 
50, then we find from formula 58) that a condenser of 3*2 
microfarad will at 10,000 volts take 10 amperes. This is 
a comparatively small current, and as its phase compared 
with that of the working current must approach more or 
less a quarter cycle, its effect on the total current cannot 
be large. As regards the lag produced by self-induction 
and consequent increase of current, this also cannot be 
very large for reasons whrch have been previously ex- 
plained. We shall probably be within the mark if we 
assume that the total current passing into the cable will 
not exceed 60 amperes. In this case the greatest varia- 
tion of potential difference between any two points of the 
cable cannot exceed 600 volts out of a total of 10,000, or 
6 per cent. If we assume that the whole capacity is 
concentrated at the generator end of the cable, we would 
under-estimate the voltage loss due to ohmic resistance 
by the amount which corresponds to the difference between 
the true current and that resulting from our assumption. 
Conversely, if we assume the whole capacity concentrated 
at the motor end, we would over-estimate the voltage loss. 
In either case the error can only be a very small fraction 
of the 600 volts lost in resistance. Under the first as- 
sumption the condenser current calculated from formula 
58) would be too large, and under the second assumption 
too small, but the error is in either case exceedingly 
small. It can be further reduced by assuming the whole 
capacity concentrated in the middle of the line as shown 
diagramatically in Fig. 98. a is the generator and m 
the motor, joined by the outgoing and retiring leads 
which form the line. We assume that the line itself has 
no capacity, but its middle points are connected with a 
condenser, k, the capacity of which is equal to that of 



284 ELECTRIC TRANSMISSION OF ENERGY. 

the real cable. The object of representing the case in 
this way is to simplify the investigation, which otherwise 
would become far too complicated for practical purposes. 
The error introduced by representing the capacity of the 
cable as concentrated in one point is, moreover, quite 
negligible in all cases likely to occur in practice. We 
have then at K a capacity of 3 2 microfarad ; between k 
and M a line resistance of 5 ohms, and between k and a 
also a line resistance of 5 ohms. The resistance of each 
armature may be taken at 2 ohms so that the total resis- 
tance in either half of the circuit is 7 ohms. The induc- 

Fig. 98. 



© =jg= fy 



tance of the motor we take at 40 ohms, and that of the 
generator at 60 ohms. 

The problem may now be represented as follows : At 
k, we have an E.M.F. of 10,000 volts effective, sending 
current at a frequency of 50, through a circuit of 7 ohms 
resistance and 40 ohms inductance, the strength of the 
current to be such as to deliver 500 Kwt. to M. At G, 
we have a generator supplying this current and that re- 
quired for the condenser, k, the generator working at 
such pressure as to produce 10,000 volts at k, the resis- 
tance being 7 ohms, and the inductance 60 ohms. Re- 
quired to find the working condition of the system. The 
solution of this problem can best be made graphically by 
means of a clock diagram. Not to complicate the matter 
uselessly, we neglect armature reaction. If required, the 
corrections for armature reaction can be made in accord- 
ance with the explanation given a few pages back. 



CAPACITY OF LINE. 



285 



Let, in Fig. 99, hh represent the hyperbola for 500 
Kwt., and let o a2 be the line of resultant E.M.F. (see 
also Fig. 90), then, by the construction explained on 
p. 260, we can find various positions of the E.M.F. radius 
of the motor, corresponding to an input of 500 Kwt. 
when the impressed E.M.F. is 10,000 volts. The ends of 
these radii lie on a curve (dotted line in Fig. 99), and we 
may select any point on that curve as the working point. 

Fig. 99. 




i-r-^r woe**. 



I I t r 



OL-nvjoe-vc^. 



Say that in order to get a reasonable margin of power we 
select the point 2? 25 corresponding with such an excitation 
as to produce 10,500 volts in the motor. From E 2 we 
drop a vertical to the hyperbola, and from its point of 
intersection we draw a horizontal to the left till it cuts 
Oa 2 in A 2 . The line A 2 JE 2 represents the impressed 
E.M.F. (10,000 volts) in the middle of the cable, and this 
put in its proper place gives us O E. The projection of 
O E 2 on the horizontal, measures 9,100 volts ; the current 
to produce 500 Kwt. must, therefore be 500,000/9,100 = 
55 amperes, and this is drawn to the left, O I v This is 



286 ELECTRIC TRANSMISSION OF ENERGY. 

the current flowing through the circuit KM. To find 
the current flowing through the circuit, G K, we combine 
with O I x the current taken by the condenser. This, at 
10,000 volts is 10 amperes, and must, in position, be at 
right angles to O E. By drawing J 2 I 2 perpendicular to 
O E, and of such length as to represent 10 amperes, we 
find the point I 2 ; and O I 2 gives, in direction and magni- 
tude, the current flowing through the generator ; this 
scales 58 amperes. There remains yet the E.M.F. of the 
generator to be determined. Draw Oa at right angles to 
O I 2 and Oa 1 at such an angle to Oa that tan a Oa l is 
equal to the ratio of resistance and inductance (in our 
case, 7/60). The E.M.F. required to balance self-induc- 
tion is 58x60 = 3480 volts. By measuring this off on 
Oa, we obtain the point A y and by drawing a line 
through A) parallel to OI 2 , we obtain the point A x and 
the E.M.F. OA^ which is the resultant between the 
E.M.F. of the generator and the E.M.F. in the middle of 
the cable. We thus find OE Y the E.M.F. to which the 
generator must be excited ; in this case, 9,330 volts. 

It is interesting to note that if the cable had no 
capacity, a similar construction to that just explained 
shows that the generator would have to be excited to 
9,900 volts. The effect of capacity is, therefore, to 
require a slightly reduced voltage of the generator, and 
a slightly increased current. 



CHAPTER IX. 

Objections to Single Phase Transmission — Advantages of Poliphase Trans- 
mission — Baily's Motor — Arago's Disk — Ferraris' Motor of 1885 — Effect 
of Rotary Field on closed Coil Armature — Theory of Rotary Field 
Motors — Magnetic Slip — Torque Diagram — Starting Power — Magnetic 
Leakage — Extension of Theory to Practical Motors — Power Factor — 
Efficiency — Examples. 

The transmission of power by means of single phase 
alternators is perfectly practicable, and is, moreover, the 
most simple and reliable system that can be employed for 
long distance work, especially if no subdivision of power 
is required. If, however, the power at the delivery end 
of the line has to be split up between a large number of 
small motors which must be capable of starting against a 
load without extraneous help, then a different system of 
transmission becomes preferable. There are two objec- 
jections against the use of small alternators as motors ; 
one is the necessity of providing some separate source of 
continuous E.M.F. for excitation, and the other is, their 
inability to start by themselves. When we have to 
deal with machines of a moderate or large size, these 
objections are of very little account. The arrangement 
usually adopted in such cases is as follows : The alter- 
nator is combined with an exciting dynamo, and a storage 
battery is provided, which, at starting, is connected with 
the exciter, working it as a motor. Thus the alternator 
is brought up to speed, and when its frequency is that of 



288 ELECTRIC TRANSMISSION OF ENERGY. 

the supply current, the latter is switched on. The right 
moment for connecting is indicated by a synchronizer, and 
after the power current is switched on, the load may 
be gradually thrown on. The alternator then supplies 
power for its own exciter, and the latter may also be 
utilized to charge up the battery ready for the next start. 
All this is simple enough, and comparatively inexpensive, 
when we have to deal with large powers, but for small 
motors the complications and cost of exciter, battery, syn- 
chronizer, and mechanical gear for throwing the load on, 
become rather objectionable features of this mode of 
working ; and hence the attention of engineers, especially 
on the Continent and in the United States has, for the 
last few years been directed towards a system of power 
transmission by alternating currents which should be free 
from these objections. The details of the machinery de- 
vised by the various inventors differ considerably, but all 
motors have this in common, that the armature is acted 
upon by a magnetic field which progresses round the 
spindle with a more or less even angular speed. Such 
motors are therefore called " rotary field motors." 
Another feature is, that no part of the motor is excited 
by a continuous current supplied from an external 
source ; and that all currents circulating in the armature 
are due to electro-magnetic induction. On this account 
such motors are also sometimes called " induction motors." 
Another term sometimes used is " poliphase motors," be- 
cause two, three, or more distinct alternating currents of 
the same frequency, but different phase, are used in 
working them. 

Without entering in detail into any question concerning 
the priority of the many patents which have been taken 
out in connection with such motors and the various 



FIRST ROTARY FIELD MOTOR. 289 

methods of working them, a short historical review may 
prove of interest. Like so many other remarkable inven- 
tions, that of the rotary field motor is much older than 
commonly supposed. As far as I have been able to 
ascertain, it dates back to the year 1879, when in a paper 
read before the Physical Society of London on the 28th 
June Walter Baily showed how Arago's Rotation could 
be produced by a number of fixed electro-magnets acting 
on a copper disk. The paper is published in the " Philo- 
sophical Magazine " of October, 1879, where diagrams 
illustrating the principle of the invention and arrange- 
ment of apparatus will also be found. The latter con- 
sisted of a copper disk suspended in the centre on a 
needle point so as to be able to revolve. Below the disk 
were placed four electro-magnets with their vertical axes 
equidistant from the centre, and their upper poles in 
close proximity to the under surface of the disk. It is 
remarkable that these magnets are shown with laminated 
cores. The exciting currents were supplied by two 
batteries, and a commutator was used to alternately re- 
verse the polarity of the field-magnets. Baily evidently 
recognized that reversals succeeding each other quickly 
will give an increased effect ; for he says : " The experi- 
ment with the four electro-magnets may be readily per- 
formed by means of a commutator which will reverse the 
current several times in a second ; and a considerable 
rotation can be given to the disk." He also recognized 
that by placing other magnets above the disk, that is to 
say, providing a closed magnetic circuit, the effect on the 
disk might be much increased. His instrument contained 
a reversing switch in one of the field-magnet circuits 
whereby he was able to produce the rotation in either 
sense. We have here all the important features of th§ 

u 



290 



ELECTRIC TRANSMISSION OF ENERGY. 



modern two-phase motor embodied in an apparatus in- 
vented fifteen years ago, but the invention had been 
overlooked, because in those days the possibility of using 
alternating currents for power transmission had not even 
occurred to engineers. 

The next important step in the development of such 
motors was made by Professor Galileo Ferraris, who, 
during the summer and autumn of 1885, has constructed 
several two-phase motors. These machines were on view 
at the headquarters of the American Institute of Elec- 

Fig. 100. 




trical Engineers at the Chicago Exhibition. One of 
these motors, built in 1885, has the form shown in Fig. 100, 
where B B l and A A x are two pairs of electro-magnets 
joined by a yoke G of iron wire. Within the polar cavity 
there is placed an armature M, consisting of a copper 
cylinder. Armatures consisting of solid iron and others 
of an iron core with a copper coating were also tried. 
The description of this motor was only published in 
March, 1888, but before then two other patents for 
motors of this kind were taken out ; one by the Helios 
Company of Cologne in May, 1887, and the other by 



THE TESLA SYSTEM. 



291 



Borel and Paccaud in February, 1888. In May, 1888, 
we have Tesla's very complete patent specification for 
power transmission by two-phase alternating current, and 
after that come a host of others. 

The production of a rotating field in the motor is 



Fig. 101. 



N 




explained by Tesla by means of diagrams some of which 
are reproduced in Fig. 101. N S are the field-magnets 
of the generator which is provided with an armature 
having two coils as shown. The field system of the 
motor consists of a ring of laminated iron surrounded by 
four coils whichare connected in pairs with the four 



292 ELECTRIC TRANSMISSION OF ENERGY. 

line wires. The armature of the motor is not shown. 
When the armature of the generator occupies the position 
shown in the top figure, only the horizontal coil is active 
and sends current through the right and left coil of the 
motor field, producing lines of force in the direction indi- 
cated by the arrow N. When the armature of the 
generator has reached the position shown in the second 
figure, both coils are active and all four coils on the 
motor magnets are energized, producing by their com- 
bined action a field in the direction of the inclined arrow. 
In the next position of the generator armature, only the 
top and bottom coil of the motor-magnet are energized, 
producing a field in a horizontal direction and so on, the 
general effect being that the field in the motor rotates 
with the same speed as the armature of the generator. It 
is obvious that a similar action is produced in the 
Ferraris motor, Fig. 100. Calling a and b the two cur- 
rents energising the magnets AA Y and BB Y respectively, 
then with a phase difference of 90° a will be a maximum 
when b is zero, and vice versa. Thus, at the moment 
when a is a maximum, the field passing through the 
armature will be horizontal ; an eighth's period later when 
the a and b currents are equal (though a is decreasing 
and b increasing), the resultant field will pass through the 
armature at an angle of 45° to the former direction. After 
a further eighth's period only the coils BB l are energised, 
and the field will have a vertical direction, and so on ; 
the resultant field revolving round the centre with a 
speed corresponding to the frequency of the supply 
currents. 

It will thus be seen how a rotating field can be pro- 
duced by the employment of two alternating currents of 
equal frequency, but having a phase difference of 90° . 



THE ARAGO DISK. 293 

If we build a Ferraris motor with three instead of two 
pairs of magnets, and energise them by three alternating 
currents with 120° phase difference between any two, we 
shall also obtain a rotary field, and so on for any larger 
number of phases. There is, however, no advantage in 
employing more than three phases, whilst the multiplica- 
tion of circuits constitutes an undesirable complication ; so 
that for practical work the choice is limited to either two 
or three phases. The system of power transmission by 
polyphase currents consists, then, of a generator or set of 
generators, producing the currents at the sending end of 
the line, and a rotary field motor at the receiving end of 
the line, the line itself consisting of at least three wires, 
as will be explained later on. For the present we shall 
confine ourselves to the motor only, and endeavour to 
establish a working theory in the same way as has 
already been done in previous pages of this book for 
continuous current and single phase alternating current 
machines. 

The well known Arago disk may serve as a starting 
point for our theory. In this instrument we have a 
copper disk mounted on a vertical axis passing through 
its centre, and so arranged that it can be set into rapid 
rotation. Over the disk, and in close proximity to it, is 
placed a compass-needle, which points north-south when 
the disk is at rest. If, however, the disk be rotated in 
either direction, the compass-needle is deflected corre- 
spondingly, and if the rotation is made rapid enough the 
needle itself is finally caused to revolve in the same 
sense. The explanation of this experiment is as follows : 
The compass-needle, being a magnet, produces through- 
out the space surrounding it a magnetic field, part of 
which passes through the copper disk. The latter when 



294 ELECTRIC TRANSMISSION OF ENERGY. 

rotating cuts the lines of force and currents are thereby 
produced in the copper. It is not necessary to inquire 
into the exact paths of these currents, which, indeed, are 
extremely complicated ; but it will be obvious that in 
close proximity to the poles these currents must be more 
or less radial, that is, at right angles to the lines of the 
field and the direction of movement. These currents 
flow, therefore, in a direction more or less parallel to the 
needle, and the latter is acted upon in the same manner 
as in the well-known Oersted experiment, where a con- 
ductor carrying a current is placed north-south either 
over or under the compass-needle. The result is that 
the needle is deflected, and if the deflection exceeds 90° 
it is set in rotation. Obviously the experiment might 
also be reversed. We might rotate the magnet, and 
then the disk would be acted upon by a certain mechani- 
cal twisting couple tending to set it in rotation. This is 
the most simple form of rotary field motor. The magnet 
produces the field, which in this case must be rotated by 
power, and the disk represents the armature of the motor. 
Such an arrangement, although useful as a starting-point 
for a theory of rotary field motors, because it facilitates 
the understanding of their action, would, of course, be 
quite useless for practical purposes. Since we must have 
mechanical power on the spot to revolve the magnet, we 
can use that power direct, and need not pass it through 
the motor at all. The motor only becomes of practical 
value when no mechanical power is available on the 
spot, and we must therefore so alter the construction of 
the machine, that the revolving physical magnet is re- 
placed by some equivalent device which receives the 
power electrically. We must, in fact, produce a rotating 
field, without factually rotating a physical magnet, and 



EFFECT PRODUCED BY A REVOLVING FIELD. 295 

this object is attained by the inventions of Ferraris, 
Tesla, and others, as already explained. 

When we rotate a physical magnet, the strength and 
configuration of the field acting upon the armature 
conductors are of course the same for all positions during 
one revolution, and to get an exact equivalent by means 
of a field electrically produced, the latter would have to 
satisfy the following conditions : (1) Strength and con- 
figuration must be independent of the direction in 
space ; (2) the speed of rotation must be constant. Now 
it is easy to see that these conditions are not fulfilled in 
the Ferraris motor, Fig. 100, and, indeed, cannot be 
fulfilled in any motor that can be practically constructed. 
If we build the motor with well defined field-poles, we 
must have a more or less jerky movement of the resultant 
field, and its strength and configuration must necessarily 
be subject to fairly large variations. Even if we avoid 
the use of pole pieces, the number of exciting coils must be 
finite, and there must be variations in the strength of the 
field. It will be shown later on that these variations 
are automatically corrected or] reduced by armature re- 
action, and are, therefore, not nearly so harmful as might 
at first sight be supposed ; but for our present purpose 
it is not necessary to enter into these details. What we 
have to determine now is whether, with a field such as 
can be produced practically, a twisting couple will be 
exerted on the armature. It is obvious that the larger 
the number of phases, the less jerky will become the 
rotary movement of the field. We shall, therefore, 
investigate the worst possible case in this respect, 
namely, a motor-field energised by two currents only 
differing in phase by a quarter period. Apart from 
armature reaction, the ratio between minimum and maxi- 



296 ELECTRIC TRANSMISSION OF ENERGY. 

mum field strength would in this case be as 1 : \/2 = 
1 : 1*41, whilst in a three-phase motor the ratio would be 

-—— : 1 = 1 : 1*16. The shape of field-magnet usually 

adopted in modern machines differs from the original 
Ferraris arrangement in this respect, that no sharp dis- 
tinction exists between magnet cores, poles, and yoke, all 
these parts being more or less merged in one cylindrical 
ring of subdivided iron. As a typical form, we may 
take a Gramme ring, as shown on the top of Fig. 102, 
the winding consisting of two pairs of coils, A and 2?, 
covering the four quarters of the ring. The supply 
leads for one current are connected to the wires a a, and 
those for the other current to the wires b b. It will be 
easily understood that the field may also be wound drum 
fashion ; but as such a winding cannot be so easily fol- 
lowed in a diagram, the Gramme winding has been 
adopted in Fig. 102. Within the field is mounted the 
armature, which consists of a cylindrical core of iron 
plates, provided with external conductors. Two of these 
conductors, forming a single coil, closed on itself as 
shown, the width of the coil being such as to embrace 
one quarter of the circumference of the armature, which 
disposition must obviously give maximum induction 
through the coil. 

The distribution of the field at various times is shown 
by the diagrams I. to IX. in this figure and in Fig. 103. 
In order to simplify the representation, the circum- 
ference of the interpolar space is straightened out, and 
the induction per centimetre of circumference is repre- 
sented by the ordinates of the broken line. The coil is 
shown below each diagram in the same position ; and 
the direction of the current induced in it by the advanc- 



EFFECT PRODUCED BY A REVOLVING FIELD. 297 



Fig. 102. 






- W 



o 

© 




(+> (0 





fO (-) 



G/ 





298 ELECTRIC TRANSMISSION OF ENERGY. 

ing field is indicated by dots and crosses in the usual 
way. The circle on the left of each figure represents 
the phase of both currents. Thus in diagram I. the cur- 
rent in A is zero, and that in B a positive maximum. 
The field produced by B passes through zero, and changes 
its sign at the circumferential points, 2 and .6. The coil 
is traversed by that part of the field which lies between 
the points 1 and 3. Since within this space half the field 
is positive and half negative, the total field passing 
through the coil at this moment is zero. By reference to 
diagram II. it will be seen that a moment after the total 
field passing through the coil has a positive value, and 
since by Lenz's law the coil must oppose this change, we 
see that in diagram I. the current must circulate as indi- 
cated by the dot and cross. The effect of this current, 
combined with the field in 1 and 3, is to produce in each 
conductor a mechanical force acting towards the right, as 
indicated by the two small arrows. 

In the position II., which occurs later than I. by one- 
sixteenth of a complete cycle, the force is still to the 
right in both wires, though greater in that under point 1, 
because the strength of the field in that point is greater 
than in 3. In the next position the current flows as 
before, but only the wire in point 1 produces a force to 
the right, the field strength in 3 being now zero. When 
position IV. is reached, we have still the same direction 
of current, but the force acting on the wire in point 3 has 
now been reversed, and opposes the force on the wire in 
point 1. In V. there is no current, and consequently no 
mechanical force ; in VI. the forces are opposed, but 
their difference is towards the right and so on. It will 
be clear from an examination of these diagrams, that on 
the whole the coil is acted upon by a mechanical force 



EFFECT PRODUCED BY A REVOLVING FIELD. 299 



Fig. 103. 



A V 

B 




-I 1 1 -Sfc < 1 H 



O P 




VI 




w 





vm 





IX 





(5ZZZZ© 



300 ELECTRIC TRANSMISSION OF ENERGY. 

directed towards the right, and tending to produce clock- 
wise rotation, that is to say, the coil will try to follow the 
rotation of the field. What has been shown here to take 
place with one armature coil, must obviously take 
place with all the armature coils, their collective effect 
being to impart to the armature a powerful twisting 
couple in a clockwise direction. 

The above explanation is sufficient to show in a general 
way how the torque in the armature of a rotary field- 
motor is produced ; but it is not sufficient for an exact 
determination of the torque, because it does not take 
account of a very important effect, namely, armature re- 
action. The lines indicating the configuration of the 
field in Figs. 102 and 103, are obviously only correct if 
the only currents producing the field are those passing 
through the coils A and B. We have, however, seen 
that the coils on the armature also carry currents, and 
these must necessarily affect the distribution and total 
strength of the field. Although this is, strictly speak- 
ing, only a secondary effect, it is by no means negligible, 
and any theory of rotary field-motors which does not 
take account of armature reaction must lead to results 
at variance with practical experience. Our next step 
must therefore be to investigate the effect of the currents 
produced in the armature conductors. 

To attempt such an investigation for the most general 
case, that is, for a field of irregular configuration and 
irregular speed, would lead to mathematical expressions 
of such complexity as to be quite useless for practical 
purposes. We must, therefore, be content with the ap- 
proximate, but at the same time much more simple solu- 
tion of the problem, which results from the assumption 
that the broken line in Figs. 102 and 103, representing 



ELEMENTARY THEORY OF REVOLVING FIELD. 301 

the configuration of the field produced by the supply 
currents, may, without serious error, be replaced by a 
true sine curve, advancing with a constant speed. In 
making this assumption, we do not violate physical 
probabilities to any great extent. In the first place the 
sharp corners of our broken line are impossible when 
there is an air space between the iron surfaces of field 
and armature. Our curve then, to begin with, must 
have the corners rounded. Next, any great variation in 
the highest point of the curve is impossible for the follow- 
ing reason. The whole surface of the armature is covered 
by coils closed on themselves. Any variation of field 
strength (apart from the variation due to the even pro- 
gression of the field), must therefore immediately produce 
in the armature conductors currents which oppose the 
change, and thus the general effect of these currents 
must be to equalize the maxima, and still further to 
round off the corners of the broken line, so that to 
assume it to be a sine curve is, after all, not such a very 
great stretch of imagination as may at first sight appear. 
That the effect of the armature currents is to obliterate 
more or less the changes in field strength is proved prac- 
tically by the fact that two-phase motors work as well 
as three-phase motors, yet in the former the maximum 
exceeds the minimum by apparently 41, and in the latter 
by only 16 per cent. 

In order to be able to deal by means of simple mathe- 
matics with the working condition of a rotary field motor, 
we assume that the induction within the interpolar space 
between field and armature varies according to a simple 
sine law. Whether this induction is due to the current 
in the field coils alone, or to the combined effect of field 
and armature currents, we need at present not stop to 



302 ELECTRIC TRANSMISSION OF ENERGY. 

inquire ; all we care to know is that such an induction 
does actually exist when the motor is at work, and that 
the sinusoidal field which it represents revolves with a 
speed corresponding to the frequency of the supply 
currents. Thus, if there be 4 field coils, as in Fig. 102, 
and the frequency is 50, we would have a two-pole field 
revolving 50 times a second, or 3,000 times a minute, 
round the centre of the armature, and if there were no 
resistance to the movement of the latter it would be 
dragged round by the field at a speed of 3,000 revolu- 
tions per minute. It is obvious that the actual speed 
must be smaller. If the speed of the armature coincided 
exactly with that of the field, then the total induction 
passing through any armature coil, or between any pair 
of conductors on the armature would remain absolutely 
constant, and there would be no E.M.F., and, therefore, 
no current induced in the armature wires. Where there 
is no current there can be no mechanical force, and the 
armature could, therefore, not be kept in rotation. In 
order that there may be a mechanical force exerted, it is 
obviously essential that there shall be a variation in the 
magnetic flux passing through any armature coil, and 
that necessitates a difference in the speed of rotation 
between field and armature. This difference is called 
the " magnetic slip " of the armature. If, for instance, 
the speed of the field in our two-pole motor, Fig. 102, is 
50 revolutions per second, and the speed of the armature 
48 revolutions per second, we would have a magnetic 
slip of 2 revolutions out of 50, or 4 per cent. In modern 
machines the slip at full load averages about 4 per cent, 
and rarely reaches as high as 10 per cent., so that good 
rotary field motors are in point of constancy of speed 
under varying load about equal to continuous shunt motors. 



ELEMENTARY THEORY OF REVOLVING FIELD. 303 

It was mentioned above that the motor shown in 
Fig. 102 would have a frequency of 50 revolutions at a 
speed only by 4 per cent, short of 3,000 revolutions per 
minute. This is an inconveniently high speed for any 
but very small sizes. To reduce the speed is, however, 
quite easy. We need only increase the number, and pro- 
portionately reduce the length of the field coils. Thus, 
if instead of 4 coils, each spanning 90° of the circum- 
ference, we use 8 coils, each spanning 45°, and connect 
them so as to produce two rotary fields, the speed will 
be reduced to one half of its former value. By using 12 
coils we obtain a six-pole motor, in which the speed will 
be reduced to one-third, or about 1,000 revolutions per 
minute ; with 16 coils we get down to 750 revolutions, 
and so on. In order to avoid unnecessary complexity 
we shall, however, commence the investigation on a two- 
pole machine, having only one revolving field, and leaving 
the transition to a multipular machine running at lower 
speed until the more simple case has been dealt with. 

Such a machine is shown in Fig. 104. The field con- 
sists of a stationary cylinder, composed of insulated iron 
plates, and provided close to the inner circumference 
with holes through which the winding passes. The 
armature is also a cylinder made up of insulated iron 
plates provided with holes near its outer circumference 
for the reception of the conductors. The use of buried 
conductors, although not absolutely necessary, has two 
important advantages — first, mechanical strength and 
protection to the winding ; and, secondly, reduction of 
the magnetic resistance of the air gap, which, it will be 
seen later on, is an essential condition for a machine in 
which the difference between the true watts and apparent 
watts shall not be too great. The armature conductors 



304 



ELECTRIC TRANSMISSION OF ENERGY. 



may be connected so as to form single loops, each passing 
across a diameter, or they may all be connected in 
parallel at each end face by means of circular con- 
ductors, somewhat in the fashion of a squirrel cage. 
Either system of winding does equally well, but as the 
latter is mechanically more simple, we will assume it to 
be adopted in Fig. 104. The circular end connections 
are supposed to be of very large area as compared with 



Fig. 104. 




the bars, so that their resistance may be neglected. The 
potential of either connecting ring will then remain per- 
manently at zero, and the current passing through each 
bar from end to end will be that due to the E.M.F. 
acting in the bar divided by its resistance. It is impor- 
tant to note that the E.M.F. here meant is not only that 
due to the bar cutting through the lines of the revolving 



RELATIVE SPEED. 305 

field, but that which results when armature reaction and 
self-induction are duly taken into account. 

Let us now suppose that the motor is at work. The 
primary field produced by the supply currents makes ~ x 
complete revolutions per second, whilst the armature 
follows with a speed of ~ 2 complete revolutions per 
second. The magnetic slips is then 

s = ~ l 1 62) 

If the field revolves clockwise, the armature must also 
revolve clockwise, but at a slightly slower rate. Rela- 
tively to the field, then, the armature will appear to 
revolve in a counter clockwise direction, with a speed of 

~ = ~i ~2 
revolutions per second. As far as the electro-magnetic 
action within the armature is concerned, we may there- 
fore assume that the primary field is stationary in space, 
and that the armature is revolved by a belt in a back- 
ward direction at the rate of ~ revolutions per second. 
The effective tangential pull transmitted by the belt to 
the armature will then be exactly equal to the tangential 
force which in reality is transmitted by the armature to 
the belt at its proper working speed, and we may thus 
calculate the torque exerted by the motor as if the latter 
were worked as a generator backward at a much slower 
speed, the whole of the power supplied being used up in 
heating the armature bars. The object of approaching 
the problem from this point of view is of course to simplify 
as much as possible the whole investigation. If we once 
know what torque is required to work the machine slowly 
backward as a generator, it will be an easy matter to 
find what power it gives out when working forward as a 
motor at its proper speed. 

x 



306 



ELECTRIC TRANSMISSION OF ENERGY. 



Let in Fig. 105 the horizontal a, c, b, d, a represent 
the interpolar space straightened out, and the ordinates 
of the sinusoidal line, b, the induction in this space, 
through which the armature bars pass with a speed of 
~ revolutions per second. We make at present no 
assumption as to how this induction is produced, except 
that it is the resultant of all the currents circulating in 

Fig. 105. 




the machine. We assume, however, for the present that 
no magnetic flux takes place within the narrow space 
between armature and field wires, or, in other words, that 
there is no magnetic leakage, and that all the lines of 
force of the stationary field are radial. The rotation 
being counter clockwise, each bar travels in the direc- 
tion from a to c to £, and so on. The lines of the field 



EFFECT OF ARMATURE CURRENTS. 307 

are directed radially outwards in the' space d a c, and 
radially inward in the space c b d. The E.M.F. will, 
therefore, be directed downwards in all the bars on the 
left, and upwards in all the bars on the right of the ver- 
tical diameter in Fig. 104. Let e represent the curve 
of E.M.F. in Fig. 105, then, since there is no magnetic 
leakage the current curve will coincide in phase with the 
E.M.F. curve, and we may represent it by the line I. 
It is important to note that this curve really represents 
two things. In the first place it represents the instan- 
taneous value of the current in any one bar during its 
advance from left to right ; and in the second place it 
represents the permanent effect of the current in all the 
bars, provided, however, the bars are numerous enough 
to permit the representation by a curve instead of a line 
composed of small vertical and horizontal steps. The 
question we have now to investigate is : what is the mag- 
netising effect of the currents which are collectively 
represented by the curve I ? In other words, if there 
were no other currents flowing but those represented by 
the curve I, what would be the disposition of the magnetic 
field produced by them ? Positive ordinates of I represent 
currents flowing upwards or towards the observer in 
Fig. 104, negative ordinates represent downward currents. 
The former tend to produce a magnetic whirl in a 
counter clockwise direction, and the latter in a clockwise 
direction. Thus the current in the bar which happens 
at the moment to occupy the position b, will tend to pro- 
duce a field, the lines of which flow radially inwards on 
the right of b, and radially outwards on the left of b. 
Similarly the current in the bar occupying the position 
a, tends to produce an inward field, i.e., a field the ordi- 
nates of which are positive, in Fig. 105, to the left of a, 



308 ELECTRIC TRANSMISSION OF ENERGY. 

and an outward field to the right of a. It is easy to 
show that the collective action of all the currents repre- 
sented by the curve / will be to produce a field as 
shown by the sinusoidal line A. This curve must 
obviously pass through the point 5, because the magne- 
tizing effects on both sides of this point are equal and 
opposite. For the same reason the curve must pass 
through a. That the curve must be sinusoidal is easily 
proved, as follows : Let i be the current per centimetre 
of circumference in b, and let r be the radius of the 
armature ; then the current through a conductor distant 
from b by the angle a, will be i cos a per centimetre of 
circumference. If we take an infinitesimal part of the 
conductor comprised within the angle d a, the current 
will therefore be 

di = i r cos a d a, 

and the magnetizing effect in ampere-turns of all the 
currents comprised between the conductor at b, and the 
conductor at the point given by the angle a will be 



/ 



a 

di= — i r sin «. 



and since the conductors on the other side of b act in the 
same sense, the field in the point under consideration 
will be produced by 2 i r sin a ampere-turns, i being the 
current per centimetre of circumference at b. 

Since for low inductions, which alone need here be 
considered, the permeability of the iron may be taken as 
constant, it follows that the field strength is proportional 
to ampere-turns, and that consequently A must be a true 
sine curve. 

When starting this investigation, we have assumed 
that the field represented by the curve B is the only field 



IMPRESSED FIELD. 309 

which has a physical existence in the motor ; but now we 
find that the armature currents induced by B would, if 
acting alone, produce a second field, represented by the 
curve A. Such a field, if it had a physical existence, 
would, however, be a contradiction of the premiss with 
which we started, and we see thus that there must be 
another influence at work which prevents the formation 
of the field A. This influence is exerted by the currents 
passing through the coils of the field magnets. The 
primary field must therefore be of such shape and 
strength, that it may be considered as composed of two 
components, one exactly equal and opposite to A, and 
the other equal to B. In other words, B must be the 
resultant of the primary field and the armature field A. 
The curve C in Fig. 105 gives the induction in this 
primary field, or as it is also called, the " impressed 
field," being that field which is impressed on the machine 
by the supply currents circulating through the field coils. 
It will be noticed that the resultant field lags behind the 
impressed field by an angle which is less than a quarter 
period. 

The working condition of the motor, which has here 
been investigated by means of curves, can also be shown 
by a clock diagram. Let in Fig. 106, the maximum 
field strength within the interpolar space {i.e., number 
of lines per square centimetre at a and b of Fig. 104), be 
represented by the line O B, and let O I a represent the 
total ampere-turns due to armature currents in the bars 
to the left or the right of the vertical, then O A repre- 
sents to the same scale as O B the maximum induction 
due to these ampere-turns. We need not stop here to 
inquire into the exact relation between O I a and O A, 
this will be explained later on. For the present it is 



310 



ELECTRIC TRANSMISSION OF ENERGY. 



only necessary to note that under our assumption that 
there is no magnetic leakage in the machine, O A must 

Fig. 106. 




stand at right angles to O l a , and therefore also to O B, 
and that the ratio between O I a and O A (i.e. armature 



FIELD A3TPERE-TURNS. 311 

ampere-turns and armature field) is a constant. By 
drawing a vertical from the end of B and making it 
equal to O A, we find O C the maximum induction of the 
impressed field. The total ampere-turns required on the 
field magnet to produce this impressed field are found by 
drawing a line from C under the same angle to C 0, as 
A I a forms with A O, and prolonging this line to its inter- 
section with a line drawn through O at right angles to 
O C. Thus we obtain O I c , the total ampere-turns to be 
applied to the field. The little diagram below shows a 
section through the machine, but instead of representing 
the conductors by little circles as before, the armature and 
field currents are shown by the tapering lines, the thick- 
ness of the lines being supposed to indicate the density 
of current per centimetre of circumference at each 
place. 

At this stage it will be convenient to indicate in 
general terms the programme of the investigation. A 
great deal has already been published in books and 
periodicals concerning the theory of rotary field motors, 
and it would have been an easy matter to simply give an 
abstract of one or the other of these theories, leaving to 
the reader the task of fitting it to practical require- 
ments. 1 Such a task may be within the power of a pro- 
fessor of mathematics, but as this book is intended for 
those who are or wish to become practical engineers, an 
abstract of existing theories, which bristle with high 
mathematics, would be of little use to them. I have 

1 One of the most admirable investigations is that recently published by 
Prof. Ferraris, " Un Metodo per la Trattazione dei Vettori Rotanti," Carlo 
Clausen, Turin. This I have only seen after my own theory was written, 
but even had it been otherwise I could not have used it, for Ferraris does 
not deal with the all important questions of current and E. M. F. in the 
supply circuits. 



312 ELECTRIC TRANSMISSION OF ENERGY. 

therefore sacrificed mathematical brevity and elegance in 
favour of a more roundabout treatment, which, although 
it occupies more space, is also more easily understood by 
practical men, because it retains in all its stages the con- 
nection between physical quantities and the formulae 
intended to represent them. The problem we have 
finally to solve concerns the working condition of a 
motor supplied with two or three alternating currents of 
given voltage. Required to know are the strength of 
supply currents, their lag, the speed, power, and 
efficiency of motor. To attempt the solution of this 
problem at one operation would be too difficult, and we 
shall therefore approach the solution gradually under 
the following programme. We assume first that we 
have to deal with a motor in which there is no other loss 
but that arising from the ohmic resistance of the arma- 
ture bars, and in which there is no magnetic leakage. 
This motor we can work under two different conditions. 
We may keep the strength of the supply currents con- 
stant, which means that the impressed field of the motor 
is a constant quantity ; or we may keep the E.M.F. of the 
supply currents constant, which means that the resultant 
field is a constant quantity. We shall then deal with a 
motor such as can practically be built. In such a motor 
there must be magnetic leakage and there must be 
various losses, the effect of which will be that if the motor 
is working on a constant pressure circuit, the resultant 
field will not be constant, but must decrease as the load 
increases, thus bringing the performance of this practi- 
cally possible motor somewhere in between the per- 
formances of the two perfect motors first mentioned. 



PERFECT MOTOR. 313 

I. Perfect Motor ; Supply Currents 
Constant. 

Going back to our original conception of the armature 
worked backwards by a belt, whilst the impressed field is 
kept constant and stationary in space, it will be obvious 
that the tangential force which must be supplied by the 
belt is proportional to the product of O B and O I a , and 
since the latter is proportional to O A, the force is 
also proportional to O A x O B, or, which comes 
to the same thing, the torque is proportional to the 
area of the triangle O C B. The E.M.F. generated 
in each armature bar, the current in it, and the collective 
current or armature ampere-turns, O I a , are all propor- 
tional to the speed of rotation and to the strength of the 
resultant field. We have therefore 

OI a =K~OB, 

where K is a constant depending on the construction of 
the machine. Let us now see what will happen if the 
field excitation O I c , remaining the same, we increase or 
diminish the belt speed, so as to vary ~ between wide 
limits. If ~ is small, it means that the machine, when 
working as a motor, will run at a speed only very little 
below synchronism ; if ~ is large, but smaller than ~ x , it 
means that the machine when working as a motor, will 
run slowly, and if ~ = ~ 1? it means that the machine is 
on the point of starting as a motor from rest. It is 
especially this latter case which is of great importance in 
the design of such machines, for their ability to start 
against a load is their chief advantage, as compared with 
ordinary synchronous alternators. 

The field excitation being kept constant, it follows 



314 ELECTRIC TRANSMISSION OF ENERGY. 

that the impressed field will remain of the same magni- 
tude, though relatively to B it will shift its direction 
as the speed ~ is raised. In other words, to each posi- 
tion of C on the circle representing the impressed 
field corresponds a particular speed ~ and a particular 
torque. Speed and torque are the two quantities of 
which we require to know the relation. 

From the above equation it will be seen that the speed 
is proportional to the ratio between OI a and OB. Now 
OI a is proportional to OA, and the latter quantity is 
equal to BC, so that the tangent of angle <p is simply a 
measure for the speed. It should not be forgotten that 
the term " speed " refers to the machine driven by belt as 
a generator on short circuit. A low speed in this sense 
means a small slip, and consequently a high speed, when 
working as a motor, and vice versa. The relation between 
speed and torque can now easily be seen from the diagram. 
The speed is proportional to tan <p, and the torque to the 
area of the triangle OCB. For zero speed (motor running 
synchronously) the area of the triangle is zero, and the 
motor gives no torque. For a very small speed (motor 
running with very little slip) the triangle is narrow and 
the torque small. If we now increase the speed (motor 
running with more slip) the torque increases to a maximum 
which is reached when <p = 45°. A further increase of 
speed again reduces the area of the triangle, and there- 
fore the torque, and the reduction is the greater the 
greater the speed. It will be clear from this that for 
stable working the slip of the motor must be such as 
corresponds to an angle <p between zero and 45°, for were 
the slip greater, then a very slight increase of load would 
bring the motor into a working condition in which the 
torque is less than before, and the motor would conse- 



TORQUE DIAGRAM. 



315 



quently stop. On the other hand, if the slip is small so 
that q> is considerably less than 45°, then an increase of 
load will bring the motor into a working condition where 
the torque is greater, and there will be no danger of the 
motor pulling up. It is obvious that if the motor is at 
all able to carry the load it will automatically adopt the 
working condition in which <g><45°. At starting the 
motor is necessarily in an unstable working condition 
because (p > 45°. The result is that the motor very 
quickly runs up to a speed not far short of synchronism, 
whilst the torque first rises to the maximum correspond- 



Fig. 107. 




ing with <p = 45°, and then drops to that value which 
corresponds with the load. 

The curve of torque as a function of the speed is 
roughly represented in Fig. 107. The exact shape 
depends of course on the constructive details of the 
machine, but the diagram is sufficient to show the general 
character. Two speed lines are shown ; on the upper 
we count the speed of the machine when driven back- 
wards by belt as a generator from right to left, and on 
the lower we count the speed of the machine when running 
as a motor from left to right. In order that the machine 
may start (~ 2 = 0, lower line), the load line must lie 



316 ELECTRIC TRANSMISSION OF ENERGY. 

wholly below the curve, and the working point will then 
be at P. The resistance of the armature bars has a very 
important bearing on the shape of the curve of torque. 
To make this point clear let us assume that we could by 
some means suddenly double the resistance of the arma- 
ture bars of the machine to which Fig. 106 refers. With 
the same resultant field and speed we would then only 
obtain half the armature amp6re-turns there shown, and 
consequently only half the armature field. To get back 
to the old conditions we would therefore have to double 
the speed ; that is to say, the tangent of the angle <p will 
now represent twice as much speed as formerly, and this 
will alter the torque diagram by making the abscissae of 
the curve twice as long as before without altering its 
ordinates. The curve so altered is shown by a dotted 
line in Fig. 107, and it will be immediately seen that by 
increasing the resistance of the armature we have also 
increased the torque at starting. At the same time the 
working point has been shifted further to the left, causing 
the motor to run with rather more slip than before, which 
means of course a greater variation of speed between full 
load and no load. The maximum torque is the same in 
either case, so that for the same load the margin of power 
is also the same ; but the motor with high resistance arma- 
ture is able to start with a heavier load. On the other 
hand, it should be remembered that high armature resis- 
tance is objectionable on account of loss of power and 
possible overheating. To avoid these defects and yet 
retain the advantage of great torque at starting the arma- 
tures of large motors are sometimes wound with several 
distinct circuits (instead of the squirrel cage winding) 
which are not closed on themselves, but connected to 
contact rings. The circuits are completed by means of 



ELEMENTARY THEORY OF MOTOR. 317 

brushes and external resistances, the latter being used 
for starting only. When the motor has run up to speed 
these resistances are short circuited. By winding the 
armature with three circuits 120° apart, the resulting 
armature field (curve A, Fig. 105) is almost perfectly 
sinusoidal, and only three contact rings are required. 

We have so far only dealt generally with the problem ; 
and to make the investigation of practical use we must 
now establish the exact numerical relation between ampere- 
turns and induction, and between induction and torque. 
We take the latter relation first. Let B represent, as 
before, the maximum value of the resultant induction in 
the interpolar space, and let the armature be wound as a 
squirrel cage with t conductors, each having a resistance 
of p ohms. The resistance of the end rings we neglect 
as already mentioned. The strength of the field at any 
point of the circumference is B sin a, the angle being 
counted from a radius at right angles to the radius along 
which the induction has the maximum value B. If r be 
the radius of the armature, and v its circumferential 
speed, we have 

v = 2 7T r ~ 

centimetres per second, and the E.M.F. generated at a 
point distant by the angle a from the point of no 
E.M.F. is 

e = B sin a v I 10 -8 

volts, if I represents the length of the armature in centi- 
metres. Since there are t bars in a length of 2 tt r centi- 

. t , t . n r d a, t 

metres, there are bars per centimetre and — 

2 7T r L 2 7T r 

bars within an element of the circumference of length 

r doc over which the induction may be regarded as con- 



318 ELECTRIC TRANSMISSION OF ENERGY. 

stant. The resistance of the group at bars within the 

element of the circumference is pi — or - — — ' and the 

1 2 7T r t da 

collective current flowing through the group of bars is 

.. #sinaW10- 8 _ 
at = r d a 

p2 7T 

amperes, or one-tenth of this in absolute measure. In- 
serting the value for v, we have the elementary current 
in absolute measure. 

di = B sin a r~l 10~ 9 r da 

P- 
The strength of field being B sin a, the tangential force 
due to the elementary group of armature conductors of 
length I is in dynes 

B 2 sin 2 a I V~10- 9 rda 

P- 
If we integrate the expression between the limits a = 
and a—7r 9 we get the tangential force in dynes exerted by 
one half the armature. The integral of sin 2 ada between 

these limits is —, and since both halves of the armature 

produce forces acting in the same sense, we find the total 
tangential force exerted by the armature to be 

p _ E l r r~ 10- 9 tk- 

P 
dynes. This expression may also be written as follows : 

„ 2w~rlB 10- 8 . t 

P = B 107 Z 2 

„ 2 m ~ r I B 10- 8 . xl 

Now is the maximum current in 

. f 
amperes passing through that bar which at the time is 



TANGENTIAL PULL OF MOTOR. 319 

in either of the two strongest parts of the resultant 
field. Call this current 7, then the above equation 
becomes 

n B II T - B II T _.. 

-dynes, or - Kilogrammes . . . 63). 



10 2 ' ' 9,810,000 2 

It is interesting to compare with this expression that 
which we obtained for a continuous current motor. 
Using the same notation, but writing c for the con- 
tinuous current in amperes, we have the tangential force 

-— — — . To make the comparison between the two 

10 7T L 

machines fair we must assume the same B in both, as 
well as the same number and resistance of conductors. 
We must also adjust the currents so as to get the same 
heating effects, and this will obviously be the case if the 
effective alternating current equals the continuous cur- 
rent or I/*/2 = c. We find thus the following relation 
between the two machines : 



Tangential Force of 
Rotary Field Motor. Continuous Current Motor. 

B clr /T BcIt 2_ 

"~10~~ V 2 10 7T 



If, therefore, the rotary field motor gives a tangential 
pull of 70^ lbs., the equivalent continuous current motor 
will only give a pull of 63| lbs. For equal weight of arma- 
ture copper the rotary field motor pulls about 1 1 per cent, 
more than the continuous current motor. In addition 
to this advantage there is the greater simplicity and 
more substantial mechanical construction. 

The armature current tends to produce a field A at 
right angles to the impressed field B. To find the 



320 ELECTRIC TRANSMISSION OF ENERGY. 

ampere-turns tending to produce the field A, we must 
integrate the current flowing through half the armature 
bars. In the point where B has its maximum value the 
current is. 7, and the current density per centimetre of 

T I 

circumference is . At a point distant by the angle 

a from the point where there is no current the current 

T I 

density is sin a, and the current in an elementary 

T I 

group of wires is - — sin a d a, which integrated over 

half the armature (« = o to a = w) gives the ampere-turns 
producing or rather tending to produce the field A, 

X«=^ 64). 

If $ is the clearance in centimetres between field iron 
and armature iron, the field which this existing power if 
acting alone would produce is 

A = WS 65 > 

lines of force per square centimetre. 

The total power developed by the armature of the 
rotary field motor is found by multiplying P with its 
circumferential speed 2 tt r ~ 2 . This gives 

BIIt 

2 " r ~*-To-2 

dyne centimetres per second, or 

w = 2 m ~ 2 r B II -J 10- 8 watts. 

Since / is proportional to the resultant field, it is evi- 
dent that the power of the motor, other things being 



POWER GIVEN OUT. 321 

equal, increases as the square of the maximum induction 
within the interpolar space. The above expression for 
Wm&y be written more simply if for 2 r Z i? we substitute 
the symbol F, signifying the total magnetic flux passing 
between armature and field. The quantity F is equiva- 
lent to what was called the total useful field passing 
through the armature in continuous current machines. 
We thus obtain 

W=7T~ 2 F10- 8 T L 

The term tt ~ 2 F 10 -8 is the maximum value of the 
E.M.F. generated in one bar if the bar passes at a speed 
of ~ 2 revolutions per second through a stationary field 
F. Call this E.M.F. E, then we have 

Let e be the effective value of E.M.F., and i the effective 
value of the current in one bar, we find the following 
simple expression for the power given out by the two 
pole armature with squirrel-cage winding : 

W=e it 66). 

In this expression the symbols have the following 
values : 

t = number of armature bars counted all round the 
circumference. 

i = effective current through one bar produced by the 
bar cutting through the field F at the rate of ~ = ~i— ~ 2 
complete revolutions per second, and given by the equa- 
tion 

i= % \ tt ~ F 10- 8 67). 

\/2 e 

where p is the resistance of one bar in ohms. 

y 



322 ELECTRIC TRANSMISSION OF ENERGY. 

e = effective E.M.F. in one bar produced by the bar 
cutting through the field F at the rate of ~ 2 complete 
revolutions per second, and given by the equation 

e= I 7T ~ 2 _F10- 8 68). 

a/2 

The power wasted in heating the armature bars is 

W. G . io ~ 

t i /?, or t t i p = — z p. bmce — = — , 

e e ~2 

it follows that the power wasted is 

In order that this may be small, ~ must be small as 

compared with ~ 2 . The slip is 5= — , and since ~ x is 

~ i 

under the usual working condition not very different from 
~ 2? we may also express the power wasted by the term 
W S, from which it will be seen that the slip given as a 
percentage is also a direct measure of the power wasted 
in heating the armature conductors. Thus, if the slip be 
3 per cent, then 3 per cent, of the power is wasted in 
heating the armature conductors. High efficiency and 
great starting torque are thus to a certain extent con- 
tradictory conditions. High efficiency means that the 
resistance of the armature must be low, making the 
slip small. The curve of torque therefore rises rapidly, 
and its tail end runs down near to the axis, so that at 
starting the torque can be but small, though when once 
running the motor is able to carry a considerable over- 
load. A large slip, which results from having an arma- 
ture of high resistance, raises the tail end of the curve of 
torque, and thus provides ample power for starting ; but 



BACK E.M.F. 



323 



the motor is rendered thereby less efficient, whilst the 
greater speed variations due to a changing load may 
also become objectionable. The general practice nowa- 
days is to design these motors for a slip of from 2 to 5 
per cent. 

It remains yet to determine the effect of the revolving 
resultant field B on the field-magnet coils. For the 
sake of simplicity we again assume that the field is 
wound gramme fashion, as shown in Fig. 108, opposite 
coils being coupled in series and traversed by the same 

Fig. 108. 




current. We limit the investigation to one of the four 
coils, say for instance the coil A. Instead of revolving 
the field with a speed of ~ x revolutions per second in a 
clockwise direction, we may imagine the field to stand 
still in space, and the coil to revolve counter clockwise 
with the same speed. Then the inner turns of the 
gramme winding will cut through the lines of the field, 
and E.M.F.'s will be induced in them. 

Let O B represent the resultant field, then the field 
strength at a is B cos (<p -f- <*) 9 and the E.M.F. acting in 
one turn of wire at a is B cos (<p + a) I 2 tt r ~ 10 — 8 
volts. The angle <p is the angle which the radius to the 



■ 



324 ELECTRIC TRANSMISSION OF ENERGY. 

centre of the coil forms at this moment with the direc- 
tion of maximum induction B. To find the instantaneous 
value of the E.M.F., not only in one turn but in the 
whole coil, we must integrate between the limits of 

a = - and a = — -r If t is the number of turns in the 
4 4 

coil, the number of turns within an element r d a of the 

2 t 
circumference is — da, and the total E.M.F. is, 



%/ 71 



e = / 5cos(? + a)/4r-^ 10- 8 d a 

7T 

~ 4 
e = B I 2 r ~ Y t 2 y' 2 cos <p 10~ 8 . 

For the two opposite coils coupled in series the E.M.F. 
has twice this value. It is a maximum for <p = o when 
the diameter joining the two centres of the coils coincides 
with the direction of maximum induction, and the E.M.F. 
is zero for <p = 90°. The E.M.F. in each set of field-coils 
varies then according to a sine function, the maximum 
value of which is 

E = ±~ l Ft </2 10- 8 

when F = B I 2 r and t is the number of wires in one 
quarter of the field. It is obvious that F represents the 
total resultant field passing between armature and field 
magnet. If the winding were concentrated in one narrow 
coil instead of being spread over two quarters of the 
circumference, the expression for E would be 2 tt ~ x F t 
10~ 8 . It will be seen that this expression is similar to 
that obtained above, except that the co-efficient here is 



BACK E.3I.F. 325 

2 7T, whereas in our previous case it was 4^2. The 
difference in the two co-efficients, namely, 6*28 in one 
case, and 5' 6 5 in the other, is due to the spreading of the 
coils over two quarters of the field circumference. Since 
the ratio between effective and maximum volts is v 2 : 1, 
we find the following expression for the effective E.M.F. 
induced by the revolving resultant field in each of the 
two field windings. 

e = l-tFtlO- 8 69) 

In this expression t represents the number of field 
wires contained in one-quarter of the circumference. The 
voltage e acts more or less in opposition to the supply 
current, and it is due to this back E.M.F. , or, to speak 
correctly, to that component of it which is in phase with 
the supply current, that the latter must deliver power 
to the motor. The total power delivered by both cur- 
rents is, 

W=2 i cos ^ 4: ~ x Ft 10- 8 

where i is the effective current in each of the two supply 
circuits, and ^ the angle of lag between supply current 
and back E.M.F. The lag is, of course, the same for 
both circuits, and is represented in Fig. 106 by the angle 
\J/. It is obvious that since <p must for stable working be 
less than 45°, ^ must be greater than 45°, so that the true 
watts given out by the motor must be something less than 
1/v 2, or less than 70 per cent, of the apparent watts 
brought in by the two supply circuits. This result 
might at first sight appear to be very unfavourable to 
rotary field motors. If this limit of <p = 45° were really 
the limit in practical machines, it would mean that the 
whole of the plant, namely, generator, line, and motor, 
would have to contain at least 50 per cent, more material 



326 ELECTRIC TRANSMISSION OF ENERGY. 

than corresponds to the maximum power actually trans- 
mitted. But it must be remembered that the case we 
have investigated does not deal with a practical machine, 
either as regards construction or method of working. As 
regards construction, the practical machine is worse than 
the one which has formed the basis of our investigations, 
because it must have certain losses not yet taken into 
account, and it must also have magnetic leakage ; as 
regards the method of working, the practical machine is 
very much better. We have assumed that the impressed 
field is constant, and this means that the supply currents 
are constant. The method of working was to connect 
the motor in series with supply circuits of constant 
current strength, and under this condition the perfor- 
mance of the machine is indeed not very satisfactory. 
The practical method of working is to connect the motor 
in parallel to supply circuits of constant potential diffe- 
rence, and on investigating this case we shall find that 
its performance is very much better. Before, however, 
passing on to this case, we must yet extend our investiga- 
tion of the constant-current motor to the relations between 
ampere-turns applied to the field coils and the resultant 
induction B. Since the latter is the resultant between 
A and (7, and since their relative positions are known 
from the clock diagram, the problem will also be solved 
if we determine the relations between field ampere-turns 
and the impressed field, supposing that no other currents 
are flowing. Thus, if we insert an armature without 
conductors, the field excitation corresponding to the 
length of line O I c in Fig. 106 would give the induction 
O (7, that is, C lines per square centimetre through the 
air gap at the point where the induction is a maximum. 
Let $ be the length of air gap in centimetres, and neglect 



FIELD EXCITATION. 327 

the ampere-turns which are required to drive the flux 
through the iron of field and armature, then 

X = -8 C 2 fr 

gives the ampere-turns to be applied to produce the 
maximum induction C. The induction actually pro- 
duced is smaller, namely B ; but since the armature 
ampere-turns act partly against the field ampere-turns, 
the latter must be provided to produce the resultant in- 
duction B. Each of the four field coils contains t wires, 
and the supply current in each circuit can now be deter- 
mined. At the moment when one circuit passes through 

zero the other should give - amperes. One-eighth 

L 

period later, when all coils carry equal currents, its 

v 

strength would be — , two neighbouring coils acting 

— t 

together. Now the maximum current corresponding 

X X 1 X 

to - — iq A /o — = — — whereas in the former 
2 t is v * 2 t s/z t ' 

phase the maximum current was — . We thus find 

that there is a discrepancy between the two methods 
of determining the current, which arises from the fact 
that with a two-phase transmission the impressed field is 
not constant. It has already been pointed out that the 
fluctuation of the field strength is prevented by compen- 
sating currents flowing in the closed winding of the arma- 
ture. These currents have no other effect than to slightly 
increase the loss in the armature due to ohmic resistance. 
To find the true field current required to produce the in- 
duction JS, we may take the mean between the two de- 
terminations. This is very nearly 



328 ELECTRIC TRANSMISSION OF ENERGY. 

i='6* C 70) 

effective amperes in each circuit. The same value 
of i is found by equating the power given to the 
field, namely 2 i e cos $,, to the power given out 

by the armature, plus loss by resistance, or W (I + — ). 

The angle + is taken from the clock diagram, Fig. 106, 
and we thus obtain 



W 



o + =) 



2 e cos %J/ y 

in which expression i and e refer to the field and not to 
the armature. 



II. Perfect Motor ; Supply Voltage 

Constant. 

The term " perfect motor " has the same meaning as 
before ; namely, a motor having no magnetic leakage 
and no losses, except the loss due to the ohmic resistance 
of the armature bars. The back E.M.F. produced by 
the revolving resultant field in the coils of the field- 
magnet must therefore be equal to the E.M.F. in the 
supply circuits, and as the latter is constant, it follows 
that the resultant field B must be constant, whatever 
may be the load on the motor. The clock diagram 
expressing the working condition of such a motor is very 
simple. 

Let in Fig. 109 O B represent, as before, the resultant 
field, and O A the field due to armature reaction pro- 
duced by the ampere-turns OI a . Then O C must be the 



SUPPLY VOLTAGE CONSTANT. 



329 



field impressed by the current in- the magnet coils, and 
O I c the corresponding ampere-turns, the angles O C I c 
and OAI a being, of course, equal. The armature 
ampere-turns are proportional to the speed ~ = ^ l — ~ 2 ? 
and the length of the line O A may therefore be taken to 
represent to a suitable scale the speed. The torque is 
proportional to the product of resultant field and arma- 

Fig. 109. 




ture current, and since the former is constant, and the 
latter proportional to O A = B (7, we find that the line 
B C may be made to represent directly the torque if the 
scale be suitably chosen. The length of this line repre- 
sents, therefore, two things, namely, speed and torque, 
from which it follows that the torque is direatly pro- 
portional to the speed ~ ; and the torque diagram is 
simply an inclined line passing through zero for ~ = O 



330 



ELECTRIC TRANSMISSION OF ENERGY. 



when ~ 2 =~ 1 ; and attaining the highest point for 
~ = ~ x when ~ 2 = O, as shown in Fig. 110. 

In the same diagram is shown the curve representing 
the power developed by the armature as a function of the 
speed. The ordinates of this curve being proportional to 
(~\ — ~ 2 ) ~2> ^ is obvious that the curve must be a para- 
bola passing through zero for ~ 2 = O at starting ; and 
again for ~ 2 =~! when the motor runs synchronously. 

Fig. 110. 




The power put into the field magnet by the supply currents 
is represented by a straight line, and the current by a 
line which is nearly straight over the greater part of the 
diagram, and slightly curved at the lower end. For 
synchronous running, when the impressed and the re- 
sultant fields are equal, the current is a minimum, and 
the lag ^ = 90°. As load is put on, the lag diminishes 
and the current increases. The power obtainable from 
the motor becomes a maximum for a slip of 50 per cent, 
when the power wasted equals that usefully given out. 



SUPPLY VOLTAGE CONSTANT. 331 

The efficiency is then 50 per cent. For a smaller slip 
the efficiency is higher, and for a larger slip lower. 

If a motor, such as we have here assumed, could be 
practically built, the working would be perfectly stable. 
To an increase of load causing a reduction of speed 
would correspond a proportional increase of torque ; and 
at starting the torque would be a maximum, which is 
just what is wanted. Such perfection is, however, not 
attainable in practice. Apart from the fact that we 
cannot build motors having no leakage, it is obvious that 
the field winding could not possibly carry the immense 
current which the motor would take at starting. In order 
to get good efficiency the motor would have to work with 
a small slip ; the working point would therefore be near 
the right hand end of the diagram, and the size of the 
field wire would be proportioned to carry the correspond- 
ing current. As a consequence this winding would not 
be capable of passing the enormously greater current 
which the diagram shows to be necessary at starting. 
The diagram merely gives the working condition of an 
ideal machine fed with current at constant pressure, in 
the same way as Fig. 107 showed the working condition 
of an ideal machine fed with constant current. The case 
of a practical machine lies between these two extremes, 
and shall now be considered. 



III. Practical Motor ; Supply Voltage 
Constant. 

To investigate the working condition of a motor, such 
as can practically be built, we have to take into con- 
sideration all the losses and imperfections of the machine. 
The losses are of three kinds, mechanical, magnetic, and 



332 ELECTRIC TRANSMISSION OF ENERGY. 

electrical, and are occasioned by journal friction, air 
resistance, hysteresis, eddy currents, and the electrical 
resistance of the field winding. The imperfections are due 
to magnetic leakage brought about by the fact that the 
magnetizing effects of the currents in field and armature 
are more or less opposed, and thus cause a certain flux 
of lines to pass along the annular space between the field 
wires and armature wires. The smaller this annular 
space can be made, that is, the smaller the clearance £ 
and the nearer the conductors are placed to the circum- 
ference, the more restricted becomes the space through 
which leakage can take place, and the more perfect will 
be the machine, but it is obvious that for mechanical 
reasons this space can never be reduced to zero. The 
effect of leakage is to set up in each conductor a counter 
E.M.F. in phase at right angles to the phase of the 
current, and in magnitude proportional to the current, 
thereby producing lag and reducing the power of the 
motor. The diagram, Fig. 109, is thus no longer correct. 
There we have assumed that the current in any armature 
bar is a maximum when that bar passes the point 
where the resultant field is a maximum. Owing, how- 
ever, to the fact that in a practical motor there must 
be a certain amount of space available for leakage 
(which is equivalent to saying that each armature bar 
has not only resistance, p, but also a certain coefficient 
L of self-induction), the current in each bar becomes a 
maximum afterthe position of maximum resultant field has 
been passed, and the line O I a in Fig. 109 will no longer 
coincide with OB, but will include with it a certain 
angle, ^. This angle increases with the speed ~, as can 
easily be seen from the following consideration. Re- 
taining our original conceptions of a stationary field in 



EFFECT OF MAGNETIC LEAKAGE. 333 

which the armature is revolved backwards by belt, and 
calling E the E.M.F. induced in each bar as it passes 
the point where B is a maximum, we have 

This is the resultant of two components ; one E s the 
E.M.F. required to overcome self-induction, and E r the 
E.M.F. required to overcome ohmic resistance. 

E s = 2tt~LI E r = P I 

when / is the maximum value of the current in one bar. 
Hence 

tan 4/ = 2 it ~ — • 

P 

Since L and p are constants for any given machine, the 
angle 4> can be determined for any speed, and having ^ 
we find the current from the relation E r =E cos ^ 

F 7T ~ 

1= cos^ 10- 8 

P 

in amperes. The effective current is 

i = I 1 * ~ F cos + 10- 8 72). 

V 2 P 

Comparing this equation with 67) it will be seen that the 
current is reduced in the ratio of 1 : cos ^, which means 
that the torque will also be reduced. The larger the 
self-induction, that is, the larger the annular space 
between the two windings, the larger becomes tan ^ 
and the smaller cos ^, so that on this account alone 
magnetic leakage reduces the power of the motor. The 
reduction does, however, not stop here. Besides the 
weakening of the torque due to reduction of current, 
there is a further weakening due to the fact that the 
maxima of current and resultant field do no longer 



334 ELECTRIC TRANSMISSION OF ENERGY. 

coincide, but differ by the angle ^. To find the tan- 
gential pull produced by one half the armature we must 

I T I 
integrate the expression B cos (^ + a) — cos a d a 

between the limits a = -and a= — — ; and to get the 

total pull exerted by the whole armature we double the 

result. This gives 

I r I 
P= B — j7L cos %[/ dynes, or 

P= 9,8^000 2~ C0S + Kil °g rammes ' • • 73 )- 

Comparing this expression with 63) it will be seen that 
for the same resultant field, and the same armature 
current the pull has been reduced in the ratio of 1 : cos ^. 
Equation 63) may also be written in the form 

2 r B II r 



rP. 



2 10 2 



or if by T we denote the torque in kilogramme-centi- 
metres 

F I T 

T = ° 74). 

39,240,000 ; 

In this expression I = amperes 75). 

In the case under consideration when there is magnetic 
leakage the corresponding formulae are 

„ Fir Ftt-IO- 6 

T = 39,240,000 C0S + and /= " ~J~ cos ^ 

FI t 

or T— ° cos 2 + kilogramme-centimetres. 

T=T cos 2 ^ 76). 



POWER REDUCED BY LEAKAGE. 335 

T is the torque which would be given by a machine in 
which there is no magnetic leakage, the armature-current 
being I . The torque actually obtained in the practical 
machine, in which there is a magnetic leakage causing 
the lag xj/, is reduced in the ratio of 1 : cos 2 4^ and the 
armature-current is reduced in the ratio 1 : cos ^. 

/— 1 cos ^. 

The power of the motor in watts is found by multiplying 
P with 2 7T r~ % 10~ 7 , and we thus find 

W=e 2 t cos 2 4^ 77), 

where i and e have the values specified in equations 67) 
and 68) respectively. Equation 77) shows that the power 
is by magnetic leakage reduced in the ratio of 1 : cos 2 «J/. 
It is therefore highly important to so design the motor 
that there shall be as little magnetic leakage as possible. 
As already pointed out this means that the air space £ 
shall not be greater than necessary to allow for free 
running mechanically, and that the holes in armature 
and field should be placed as near the circumference as 
possible. 

The angle -^ is not a constant, but varies with the 
speed ~. Under normal running conditions ~ is small 
and ^ is therefore also small. The reduction of torque 
owing to magnetic leakage is therefore less important, once 
the motor has attained its normal speed ; but at starting 
when ~ = ~ D the angle ^ is large and cos 2 \p consequently 
very small. It follows that magnetic leakage is particu- 
larly detrimental because it reduces the starting power of 
the motor. How great this reduction is depends on the 
relative values of p and L. As will be seen from 75) p 
should be small in order to have a large armature-current, 
and therefore a large torque and high efficiency when 



336 ELECTRIC TRANSMISSION OF ENERGY. 

running at normal speed. On the other hand, if p be 
very small ^ becomes large, and the torque at starting is 
too much reduced. The two conditions are to a certain 
extent contradictory, and the difficulty is solved in prac- 
tice by making p large at starting and reducing it 
gradually as the motor attains its proper speed. For this 
purpose the squirrel cage winding is in larger machines 
replaced by a winding consisting of three coils set 120° 
apart, which are connected amongst each other, and to 
three insulated contact rings on which there are three 
brushes. The brushes are connected with three non- 
inductive rheostats, and at starting the whole of the 
resistance is used. As the motor gets up speed the 
resistance is gradually reduced and finally short circuited. 
We have hitherto tacitly assumed that the resultant 
field B remains the same under all working conditions of 
the machine ; but this is obviously impossible when the 
E.M.F. of the supply current is kept constant, which is 
the only case of practical importance. Owing to self- 
induction and resistance of the field-coils an increase 
of current is necessarily accompanied by a decrease in 
that component of the supply voltage which is in phase 
with B, and consequently the total field F in 74) and 75) 
is not a constant, but becomes smaller as the supply 
current increases. This again causes a reduction in 
torque which we now proceed to investigate. To facili- 
tate the investigation we neglect at first hysteresis, eddy 
current, and mechanical losses, or rather we substitute 
for them a certain power expressed in watts which we 
deduct from the power given out by the machine. Since 
the speed of the machine under normal working conditions 
is very nearly constant, the total of these losses (which in 
any case amounts only to a small percentage of the total 



FIELD CURRENT AND IMPRESSED FIELD. 337 

power) may be considered constant. The net power of 
the machine is to be found by deducting this constant 
loss from the total power. The problem may now be 
stated as follows. 

Given a certain supply voltage and frequency, to find 
the torque and the power at different speeds of the arma- 
ture. The first question to be investigated concerns the 
relation between field current and impressed field and 
between resultant field and back E.M.F. This has 
already been done for a two-phase field and we now pro- 
ceed to apply the same treatment to a three-phase field, 
assuming for the sake of simplicity that the winding is so 
arranged as to produce a two-pole field. In Fig. Ill is 
shown a gramme ring, wound with three pairs of field- 
coils, the angular distance between two neighbouring 
coils being 60°. If the winding were drum fashion there 
would be three single coils (not pairs) set 120° apart. 
The magnetic effect is the same ; but we adopt the 
gramme winding as more easily shown in the diagram. 
The diagram is constructed in the same way as Figs. 102 
and 103 and needs no further explanation. It will be 
seen that the broken line representing the strength of the 
field at different points of the circumference approximates 
fairly closely to a sine curve. The locality of the poles 
produced is in each case indicated by thick lines, thus 
showing at a glance how the poles advance with the 
changing phases of the three-field currents. It will also 
be noticed that the number of ampere-turns producing 
maximum induction at the poles varies between narrow 
limits, namely, 2 It and \/3 It, when / is the maximum 
current in each circuit and t the number of active wires 
in one coil, or one-sixth the number of wires counted 
over the whole circumference. This term applies, of 

z 



338 ELECTRIC TRANSMISSION OF ENERGY. 



Fig. Ill, 











— 



FIELD CURRENT AND IMPRESSED FIELD. 



339 



course, equally to a drum-wound field. The average 

exciting power producing the field is the mean between 

these two values, or 1*865 /£, and if for the maximum value 

of the current we insert the effective value i, we have the 

exciting power in ampere-turns supplied by the field 

coils 

X c =2-635a. 

The current required in each of the three branches to 
produce a field excitation of X c ampere-turns is therefore 



t = -38-< 

t 



78), 



It is interesting to compare this expression with 70) 
which gives the current required in a two-phase field. 
In that case t is one quarter the total number of field 
wires T instead of one-sixth as in a three-phaser. Let us 
now assume that we have two fields of exactly the same 
size and containing the same total number of wires T, 
but arranged in one case for two and in the other for 
three phases. The field currents will then be 

jr 

z = 2*28—^ in the three-phase machine, and 

2 = 2*40^ in the two-phase machine. 

The current in the three-phase machine is thus by five 
per cent, smaller than in the two-phase machine, and the 
area of the field wire for equal resistance loss might be 
reduced by five per cent. As far as weight of copper in 
the field goes the three-phase arrangement gives thus a 
slight advantage. It also gives a slight advantage as 
regards power, inasmuch as the counter E.M.F. produced 
in a given number of turns is somewhat greater, as can 
be seen from the following consideration. Let <p be the 



340 ELECTRIC TRANSMISSION OF ENERGY. 

angle which the radius to the centre of a field coil 
includes at a given instant with the direction of B, and a 
the angular distance of an element of winding from the 

centre of the coil. Since w T ithin an angle of — there are 

o 

3 

t wires, there must be — t d a wires within an angle of 

d a. The induction in the point occupied by the 
elementary group of wires in B cos (a— <p) and the E.M.F. 
produced is 

3 

d e = B cos (<x— (p) 2 tt r~ x I— t da. 

7T 

7T 

This equation integrated between the limits of - and 

TT 

— g g^es 

e ;= JB2 r I ^ L 3i cos q> 

in absolute measure. The E.M.F. induced in one field 
coil is therefore a sine function having the maximum 

JE = F ~ x 3 t. 

In the opposite coil, belonging to the same pair, an equal 
E.M.F. is, of course, induced, and since the two coils are 
coupled in series, we have the E.M.F. induced in each 
circuit given by 

E=Q i^- t 10- 8 volts. 
This is the maximum value ; to find the effective value 
we divide by v 2, and obtain 

£ = 4-26 ~ x F t 10- 8 volts ...... 79) 

The coefficient found in 69) for the E.M.F. induced in 
one circuit of a two-phase field was 4 ; now the coefficient 
is 4*26, showing that for the same total field and the 



ADVANTAGE OF THREE PHASES. 341 

same number of turns per circuit, the back E.M.F. in a 
three-phaser is 6^ per cent, greater than in a two-phaser. 
To make the comparison between the two machines fair, 
we must, however, not assume t to be the same in both. 
We have two equal fields wound with the same total 
number, T, of wires, but connected up for three and two 
phases respectively. Let i and e refer to the two-phaser, 
and i l and e l to the three-phaser, then if the size of the 
field wire be the same in both, we have i l = l'05 i as 
previously shown. In the two-phaser we have 
e = ~ l5 F T 10 — 8 , and in the three-phaser we have 
e l = -71 ~ X F T\0-\ so that 

^ = •71 e. 

The apparent watts in each circuit of the two phases 
are w = e i, and those in each circuit of the three-phases 
are w 1 = e l i l ; and the total watts in all the circuits collec- 
tively are : 

W=2 ei. 

W l = 3 e 1 i\ 

W X = Z x 1-05 zx-71 e. 

m = 2'23ei. 

fF l = l-115 W. 

For the same expenditure of material, therefore, the 
three-phase motor will give about 11 per cent, more 
power, or to put it another way, a three-phase motor can 
be built about 10 per cent, lighter than a two-phase 
motor of the same power and speed. 

In Fig. Ill the three field circuits are shown entirely 
distinct from each other, and if arranged in this way six 
wires are required between generator and motor. The 
number of wires can, however, be reduced to three if the 
circuits are connected, as in Fig. 112. The coils form- 



342 



ELECTRIC TRANSMISSION OF ENERGY. 



ing one pair are cross connected as before, thus leaving 
six free terminals. Three of these are connected together 
by the wire o 9 and the three others, marked a b c, are 
connected with the three line wires. It is easily seen 
that with this arrangement (commonly known as the 
" star coupling," on account of the three circuits 
radiating, as it were, from the electrical centre o of the 
star), the exciting power of the coils on the field iron is 



Fig. 112. 



K 




precisely the same as with three totally independent 
circuits. The reason is, that the sum of the currents, 
a + b + c, must at all times be zero, and that by bunching 
the three return wires into one, this latter would have to 
carry zero current, and may therefore be omitted alto- 
gether. The common centre o is generally earthed, by 
which means the potential of each line wire is kept 
within the limit corresponding to the voltage of the 
generator. There is another method of coupling up the 
field coils. This is shown in Fig. 113, and is called 



STAR AND LINK COUPLING. 



343 



" link coupling." In this system there is no electrical 
centre which can be earthed, but the coils are connected 
to form a triangle or closed link, tapped by the line 
wires in three points electrically equidistant. On 
examining the diagram, and tracing the currents 
through the coils, it will be found that the excitation 
differs from that given by the star coupling. At the 



Fig. 113, 




moment when one current, say a, passes through zero, 
the other two, b and c, produce an excitation of 1*3 It 
ampfere -turns, whilst a twelfth of a period later, when b 
is a maximum and a and c have half the maximum 
value, the excitation is / 1. The fluctuation of exciting 
power is thus considerably greater with the link coup- 
ling than with the star coupling. It is interesting to 
compare the two windings by means of the following 
table : 



344 ELECTRIC TRANSMISSION OF ENERGY. 

Field excitation in ampere -turns 
produced by coupling as a 

Star. Link. Combined. 

Any current passes through 

zero value . . . 1*73 /^ IS 1 1 V515 1 1 
maximum value . . 2 I t l 1 1 1*500 It 

If by tj we denote the number of wires in one-sixth of 
the field in circumference when coupled as a star, and by 
t the corresponding number when coupled as a link. 
To produce the same average excitation, t must be 
greater than £ 13 the relation being t = 1*61 t x . The 
variation in the exciting power applied to the field has 
the effect of calling forth in the armature conductors 
compensating currents whereby the variation in field 
strength is nearly completely prevented. These com- 
pensating currents must, however, waste some power, 
and to obviate this defect Mr. Dobrowolsky has devised 
a combination of the two systems of winding under 
which the ampere-turns applied to the field remain 
practically constant. 

If t = t l + t is the number of wires in the star and 

link winding collectively, and we make t x = t =~, the 

combined effect of the two windings is therefore 1*515 It, 
and 1*500 1 1 5 as shown in the third column. The greatest 
variation from the mean exciting power is therefore 

With star coupling . . . . • 7i per cent. 
With link coupling . . . . .13 „ 

With Dobrowolsky coupling . . h „ 

With two-phase current the variation is . 1 7 „ 



We have now all the data required to determine the 
working condition of the motor by means of a clock 



TORQUE A FUNCTION OF THE SPEED. 345 

diagram. The relation between self-induction and re- 
sistance of armature bars is supposed to be known, so 
that the lag ^ of armature current behind the resultant 
field B can be determined for any speed ~, the term 
speed being here applied to signify the relative speed 
between field and armature. The total field F and the 
maximum induction B are chosen as high as considera- 
tions of efficiency and heating limits will allow. The 
clearance ^ being: known, we can from 

X t = B 1-6 3 

determine the resultant ampere-turns required to produce 
the maximum induction B. The two components are 
armature ampere-turns 64) and field ampere-turns X c . 
The latter is found graphically, and the corresponding 
field current is given by 78), whilst the effective back 
E.M.F, in one field circuit is found from 79). The 
position and magnitude of the impressed E.M.F. can 
also be found graphically if resistance and inductance 
of the field winding are known. In this construction we 
find the impressed E.M.F. and field current to produce 
a certain B at a certain speed ~. This is, however, not 
the form in which the problem is met with in practice. 
What we want to know is torque and power as a function 
of the speed ~ if the impressed E.M.F. has a constant 
value given beforehand. The transition from one solu- 
tion to the other is, however, very simple. We assume 
a certain B and ~, and find the impressed E.M.F. If 
this differs from the given value we need only enlarge or 
reduce all the lines in the diagram in whatever proportion 
is required to make the impressed E.M.F. come out at 
the correct value. 

Fig 114 shows a clock diagram so constructed. All 



346 



ELECTRIC TRANSMISSION OF ENERGY. 



the constants of the machine being known, we find the 
angle ^ for any speed ~ from 

. o L 

tan \p = 2 7T ~ — ; 
? 
hence the speed can be plotted on the vertical S S, which 

is placed at a distance from O equal to r ? the scale 

for ~ being arbitrarily chosen. 

We assume a certain induction B or total field strength 

Fig. 114. 




F 9 and find the armature current / in amperes from either 
of the two following equations : 

F 7T ~ 

1= cos + 10- 8 . 



/=— ysin^ 10- 8 , 



WORKING DIAGRAM. 347 

The latter is the more convenient expression, as it per- 
mits to read off the value of i" by means of a circle of 

F 10- 8 
radius . We can now calculate the armature 

amp6re-turns 

7T 

and plot the corresponding value on the radius O A. Let 
this be O a. Let to the same scale O b represent the 
amp&re-turns required to produce the resultant induc- 
tion B y so that 

0J = 1'65J; 

then the length O c gives to the same scale the field 
amp6re-turns X c . To find the current in each field coil 
we have for a three-phaser 

i - .38 — c . 

The loss of pressure by ohmic resistance in each field 
circuit can now be calculated, and plotted on the line 
O c to a suitable volt-scale. Let this be Or; and let 
e s = r s represent to the same scale the E.M.F. required 
to balance self-induction in the field circuit. The 
numerical value of this E.M.F. can be found if the co- 
efficient of self-induction is known, the frequency being, 
of course, ~ x . The back E.M.F. produced by the 
resultant field, F 9 is given by 

6^ = 4-26 ~j Ft 10- 8 , 

and must be plotted to the right from s, giving the total 
supply E.M.F. e—OEy which is in advance over the 
current by the angle <p. The total power supplied is 

W= 3 e i cos (p. 



348 



ELECTRIC TRANSMISSION OF ENERGY. 



Since for a constant field the torque is proportional to 
/ cos aj/, it is obvious that the length of the line T 
(which is drawn at right angles to the radius O A), gives 
to a suitably chosen scale the torque corresponding to 
any speed ; always provided that the field is really con- 
stant. This, however, cannot possibly be the case. The 
only constant quantity in the working of the motor is the 
supply E.M.F. If, then, the length O jE, resulting from 
the above construction, is either greater or smaller than 
the given value of the supply E.M.F., all the lines of the 
diagram, with exception of O S and S S, must be 

Fig. 115. 




reduced or enlarged in proportion, the angles remaining 
unaltered. Call m the ratio between the given supply 
E.M.F., and that resulting from the diagram, then the 
true currents and true volts will be m times the corre- 
sponding values as plotted in the diagram ; the true 
induction will be m B and the true field m F. The 
power put into the motor will be m 2 , W 9 and the true 
torque will be m 2 T. The true torque and power given 
out can now be plotted as a function of the speed over 
the line S S. The problem is thereby solved. 

It is interesting to note the great effect which mag- 



EXPERIMENTS WITH MOTORS. 349 

netic leakage (self-induction in armature and field) has 
upon the performance of such a motor. The curve A x in 
the torque diagram, Fig. 115, refers to a motor in which 

2 7T L 

■=•() 2, and the E.M.F. of self-induction in the field 

P 
at full load is 15 per cent, of the supply E.M.F. The 

curve A 2 refers to a motor in which both these values are 
doubled. 

Up to the present we have assumed that the self- 
induction in the armature and field is known. For 
obvious reasons it is, however, impossible to obtain it 
merely by calculation, and we must have recourse to 
experiment, so as to obtain data which can be used in 
future designs. Suppose a motor is made and ready for 
testing. Run it at full load, and note the current and 
supply voltage. This gives us the length of the lines O C 
and O E in Fig. 114, but not their relative position. To 
find this we must measure the power supplied, so as to 
determine the true watts, and the ratio of true watts to 
volt-amperes is the cosine of the angle of lag, or as it is 
also called the "power factor " of the motor at full load. 
Having found the angle <p, we can complete the diagram 
from the known data of the motor, and thus find the 

angle 4y which determines the ratio — . 

The self-induction in the field can be determined ap- 
proximately by the following experiment. Let the 
armature spindle be gripped tightly, so that it cannot 
turn, and reduce the supply voltage to such an extent, 
that under this condition no more than the full working 
current passes through the field winding. We have now 
~ = ~ }} and owing to this high frequency, an extremely 
feeble resultant field, B 9 will suffice to produce very 



350 ELECTRIC TRANSMISSION OF ENERGY. 

large armature currents. That is to say, in Fig. 114 the 
length of the line O b will shrink to almost nothing, and 
the back E.M.F. (length of line S E) will also approach 
zero. Since the loss through ohmic resistance of field 
coils is under all circumstances very small, the length of 
the line O E will become very nearly equal to the length 
of r s, or in other words, the measured volts give approxi- 
mately the E.M.F. of self-induction at the current then 
passing, which by the condition of the experiment is the 
normal working current at full load. The maximum 
strength of the resultant field may be found by running 
the motor light at normal voltage. In this case an 
extremely feeble current in the armature bars will suffice 
to keep the armature in motion, and the ampfere-turns in 
the armature will be so small as to not seriously react 
on the field. The line O C will then become vertical, and 
the E.M.F. of self-induction, and the back E.M.F. will 
come into line, so that the supply E.M.F. is the sum of 
the two. Since the E.M.F. of self-induction for any 
current can be determined by the experiment previously 
described, we are able to determine the back E.M.F. as 
the difference between the supply E.M.F. and the 
E.M.F. of self-induction. Having the back E.M.F. and 
knowing the field winding, we can easily find the total 
strength of the resultant field from the formulas pre- 
viously given. 

It is thus possible to determine approximately by a few 
simple experiments some of the electrical data which 
cannot be found beforehand by calculation. To investi- 
gate the working condition of a multiphase motor 
thoroughly, more elaborate experiments must, of course, 
be made, and amongst these the most important is the 
direct determination of the stray field or leakage when 



EXPERIMENTS WITH MOTORS. 351 

the motor is running free and loaded. The ratio of the 
flux actually utilized in the armature to that produced 
by and passing through the field coils is termed the 
leakage factor, and it will be obvious that the nearer 
the leakage factor is to unity the smaller is the self- 
induction in armature and field, and the more perfect is 
the motor. 

The following experiment for the direct determination 
of the leakage factor has been made by Mr. E. Kolben 
on a 9 horse-power six polar three-phase motor. The 
field winding consists of thirty-six coils of seven turns 
each, and the armature winding of ninety bars in holes 
arranged in six polar drum connections so as to form three 
independent circuits each closed in itself. For the leakage 
test at no load the proper armature winding is replaced 
by an experimental winding passing through only thirty 
of the ninety holes, with two wires to each hole, and all 
connected in series with the two free ends brought to a 
voltmeter. We now have in each phase of the field 
7 x 12 = 84 turns, and in the armature 60 turns. The 
field is supplied with current at a given voltage and 
frequency, and the E.M.F. induced in the experimental 
armature winding is observed on the voltmeter. The 
armature is turned slowly by hand so as to occupy 
different positions relatively to the field, and readings 
of the induced E.M.F. are taken at these different 
positions. 

Owing to the three-phase winding, these readings vary 
very little, their average being in the present case 60*5 
volts. We thus know that a magnetic flux of such 
strength is passing through the armature as to produce an 
effective E.M.F. of 60'5 volts in the 60 turns of the arma- 
ture coil. At the same time a somewhat larger flux is 



352 ELECTRIC TRANSMISSION OF ENERGY. 

passing through the field coil of 84 turns, and produces a 
back E.M.F. of 98 volts as observed on the voltmeter 
connected across the terminals of the field coil. If the 
flux were the same in both coils then the voltages should 
be in the same ratio as the windings, but as some of the 
flux is lost by leakage between field and armature, the 
E.M.F. in the armature coil is correspondingly reduced. 
We have thus, 

Leakage factor = — x -— — = -865. 
& 60 98 

For every 1,000 lines generated in the field, 155 lines 
are lost in leakage between the field and armature wind- 
ing. This applies to the condition of the experiment 
when no sensible current passes through the armature ; 
it applies of course also to the motor provided with its 
proper armature if the latter is running free, because also 
in this case the armature current is extremely feeble. It 
does, however, not apply to the case when the armature 
is running under a load, because the field and armature 
ampere-turns are then much increased and the magnetic 
pressure producing leakage is also much increased. To 
find the leakage in this case the motor was fitted with its 
proper armature and an exploring coil of 8 turns was 
placed over one of the field poles, and as close as possible 
to the armature, and the E.M.F. produced in the ex- 
ploring coil was observed with the motor running free and 
loaded. The fall of E.M.F. when the motor was loaded 
is an indication of the amount by which the leakage factor 
has been reduced. 

The following table gives a summary of the experi- 
ments. 



EXPERIMENTS WITH MOTORS. 



353 



Remarks. 


T5 
ft 

m 




o 


Current in 
Field. 


E.M.F. in- 
duced in 


Watts 
absorbed. 


Leak- 
age 
Factor. 




■5! .2 


Arma- 
ture 
Coil. 


Explo- 
ring 
Coil. 


Not running . 

Running free . 

Over loaded to 

12*5 H.-P. . 



980 

930 


50 
49 

49 


98 
98 

98 


20*2 
22-3 

457 


60-5 


26 
24*5 


365 
500 

10,260 


•865 
•865 

•815 



The leakage factor at overload is found by multiplying 
the leakage factor at no load ( # 865) with the ratio of the 
voltages of the exploring coil. The efficiency of this 
motor at 12*5 horse-power is 90 per cent, and the power 
factor is the ratio of the watts absorbed to the volt amperes 
supplied, or 

10,260/3 x 98 x45-7 = -775. 

Mr. Kolben has also tested some larger three-phasers on 
the brake with the object of determining the efficiency, 
slip and power factor. The results of the tests of two of 
these machines are given in the annexed table. 



A A 



354 



ELECTRIC TRANSMISSION OF ENERGY. 



IX. 


Notes. 


Motor I. 
Theoretical speed 
750. Squirrel 
cage armature. 
A. E. G. make. 


Motor IT. 
Theoretical speed 
750. Drum arma- 
ture with 1 1 divi- 
sions, each div. 
short-circuited in 
itself. 
Oerlikon make. 


Efficiency 
Watts II. 

Watts VI. 


1— I Tfr< CO | 

OS 00 GO 

6 6 6 


0-94 
0-905 


1— 1 
1— 1 

> 


31 i 


-f i i 

^cp 

CM r-i 


O 

o o 

TfWO 


vi. ; vii. 


Coefficient 

True 
Watts VI. 

Voltamp. 
V. 

("Power 
factor.") 


0-844 

0-81 

0-655 


0-84 
0-83 
0-145 


Real Watts 

intake, 
measured 
at motor 
terminals 
by Watt 
meter. 


48,300 
36,800 
17,700 


42,100 

37,440 

1,710 


> 


Apparent 

Watts 

3 x Volts 

IV. x Amp. 

III. 


o o o o 

tH CO o o 
CM CO © *C 

c\ «>i «i #\ 

X- *o *"- OJ 

*0 ^ <M CM 


50,220 
45,000 
11,760 


> 

M 


Volts 
betw. 
the 
neu- 
tral 
and 
each 
term- 
inal. 


© © © © 
CO CO CO CO 


CO vo GO 
OS OS o$ 


III. 

Current 
in each 
branch 
Am- 
peres. 


GO CM © iC 

fH io >0 (M 

CO (M H H 


© GO © 
GO *C ^h 
i— i r- ( 


M 


Watts 

equiv. to 

eff. H.-P. = 

736 x Eff. 

H.-P. I. 


© © © 
CO -h CM 

h Oi N O 

T^ ©" Th" 
Tf CO r— 1 


39,600 

33,900 




H 


Metric . 
H.-P. at 
the brake 
of arma- 
ture 

pulley. 


© cm © © 
CO ^H CM 


GO 

co co © 



CHAPTER X. 

Single Phase Motor — General Explanation of its Working — Theory of 
Single Phase Motors — Self-induction necessary — Torque Diagram — 
Practical Examples — Starting Device. 

If an armature with short circuited winding is placed into 
an oscillating field produced by a single phase alternating 
current, it shows no tendency to rotation as long as it is 
left to itself. If, however, such an armature be started 
in either direction, and the speed gradually increased by 
the application of external power, a point is soon reached 
when the armature of itself continues to revolve in the 
same direction, running faster and faster until syn- 
chronism is nearly reached. A load may then be thrown 
on, and the machine worked as a motor. The reason 
why the armature once set in rotation developes a torque 
in the same direction, may be explained, in a general 
way, as follows : Let the lines of the oscillating field be 
vertical, and consider one single turn armature coil of 
area A, which at a given moment includes the angle /3 
with the lines of the field. If B is the maximum induc- 
tion, the total flux passing through the coil at the time t, 
is B A sin a sin 0, where a = 2 w ~ t. The E.M.F. 
generated in the coil is 2 7r ~ B A sin jS cos a 10 -8 , and 
this will produce a certain current, depending on the re- 
sistance and self-induction of the coil. Let us first 
assume that the coil has no self-induction, but only 



356 ELECTRIC TRANSMISSION OF ENERGY. 

resistance. The current will then be in phase with the 
E.M.F.,that is to say, in the clock diagram, Fig. 116 the 
current-line O /will be at right angles to the line of in- 
duction O B. The maximum value of the current is 

/= 2tt~ B A sin/3 10~ 8 

f 
if by f we denote the ohmic resistance of the coil. Now 
the inter-action between this current and the field pro- 
duces horizontal forces acting alternately to the right 
and left, and the first question to consider is whether these 
forces integrated over the time of a complete period will 

Fig. 116. 




produce a turning moment. The turning moment at the 
time, t = a/2 9r^,is obviously proportional to Ism aZ?cosa, 
and the average effect over a complete period is propor- 

>2tt 



■/■ 



tional to ~ I sin a cos a d a. This integral is zero, and 

J o 

it follows that the coil will have no tendency to turn 
in either direction. 

This, however, is opposed to experiment. We know 
that if we place a coil at an angle to the lines of an 
oscillating field it has a tendency to set itself parallel to 
the lines. The reason of the discrepancy between theory 
and experience is that our assumption, that the coil has 



SINGLE PHASE MOTOR. 357 

no self-induction, was wrong. The effect of self-induc- 
tion is to retard the current so that the current-line in 
Fig. 116 will not be at right angles to OB as assumed, 
but will occupy the position O J 1 , lagging behind the 
E.M.F. line by the angle (p. The turning moment at 
the time t is therefore proportional, not to sin a cos a as 
previously stated, but to sin a cos (<p — a), and the 
average effect over a complete period is proportional to 

2?r 



-/■ 



sin a cos (<p — a) d a = ~ tt sin (p. 

There will thus be a torque exerted on the coil, and the 
latter will, if left to itself, assume a position parallel to 
the direction of the field. It is easy to see that for a 
complete armature, the whole surface of which is covered 
by coils, the torque will be clockwise for half the coils, 
and counter-clockwise for the other half, so that no re- 
sultant torque is produced as long as the armature is at 
rest. It is also obvious that if the resistance is small, 
and the self-induction fairly large, the angle <p will 
approach 90°, that is to say, the armature currents pass 
through their maximum values very shortly before the 
field passes through its maximum value, the combined 
effect of all armature currents being of course to oppose 
the field which induced them. Let, in Fig. 117, the 
circle represent a section through the armature bars 
(shown for simplicity as a continuous sheet of copper), 
then at the moment that the field passes through its 
maximum value, and is directed vertically downwards, 
there will be a downward current through all the bars 
lying to the right of the vertical diameter, and an upward 
current through all the bars on the left of that diameter. 



358 



ELECTRIC TRANSMISSION OF ENERGY. 



The mechanical effect due to the inter-action between 
the field and the currents is as follows : Quadrant a b 
tends to pull the armature round in a clockwise sense, 
quadrant b c tends to pull it round counter clockwise. 
In the lower half quadrant c d is acting clockwise, and 
quadrant d a counter clockwise, the net result being that 
the armature remains at rest. Now let us suppose we 
rotate the armature by mechanical power in a clockwise 
sense, and see what happens. If there were no self-in- 



Fig. 117. 



Fig. 117*. 





^ 


ct^- — 


J^ 


a>( 




\c [ \ 








/ A \ / 


\ r 






/ ct\. 


_-^c 




cL 







duction, it is obvious that not only would the currents 
pass through their maxima at the times that the field 
passes through zero, and therefore each quadrant taken 
by itself could produce no effect, but the currents would 
remain symmetrically distributed in space on either side 
of the vertical diameter b d, no matter how fast the arma- 
ture is turned. Since, however, there is self-induction, 
this symmetrical distribution will be disturbed. A cer- 
tain time must elapse from the moment that the applied 
E.M.F. has reached its maximum to the moment that 
the current produced thereby has reached its maximum. 



SINGLE PHASE MOTOR. 859 

At the moment that the field passes through zero, the 
E.M.F. is a maximum, but the current will only attain 
its maximum value something short of a quarter period 
later. If, in Fig. 117, we assume that the field is just 
passing through zero and about to grow vertically down- 
wards, then the E.M.F. will be directed downwards in 
quadrants b c and c d, and vertically upwards in quad- 
rants d a and a b. The corresponding currents cannot 
be produced instantly, but require a certain time till 
they reach their maximum values. During that time 
the armature has turned through a certain angle and 
attained the position indicated in Fig. 117*. At this 
instant we have very nearly maximum field strength, the 
lines being directed downwards, and we have maximum 
currents, which are downwards in b c d and upwards in 
d a b. The turning force produced by these currents is 
obviously clockwise in the region h a b and g c d ; and 
it is counter clockwise in the region d h and b g. The 
clockwise force is necessarily the greater, and for low 
initial speeds must increase with the speed. It is there- 
fore necessary that the initial speed should reach a cer- 
tain value before the resultant torque has become large 
enough to overcome the frictional and other resistances 
opposing rotation. This value passed, the torque increases 
and the motor runs quickly up to a speed not far short of 
synchronism. 

The above explanation of the working of a single phase 
motor makes no pretence to completeness or scientific 
accuracy. It is merely given to show, in a general way, 
how it is that such a motor can work at all, and to draw 
attention to the fact that self-induction in the armature 
is an essential condition of its working. 

The same conclusion is reached when treating the 



360 ELECTRIC TRANSMISSION OF ENERGY. 

subject in the manner first adopted by Professor Ferraris, 
which is based on the fact that magnetic fields are vector 
quantities, and may be combined in the same way as are 
forces in a parallelogram. An oscillating field may, 
therefore, be considered to be the resultant of two equal 
constant fields revolving in opposite directions, with a 
speed equal to the frequency of the oscillating field. 
Thus, if we have a field oscillating with a frequency of 
50 between the values F— 100,000 and F = -100,000 
e. g. s. lines, we may imagine this replaced by two 
fields, each giving a constant flux of F = 50,000, and 
revolving with a frequency of 50 in opposite directions. 
Now imagine that field 1 revolves clockwise and 
field 2 counter clockwise ; imagine also that the armature 
is rotated clockwise by power at a speed of 50 revolu- 
tions per second. The armature conductors will then 
relatively to field 1 be at rest, and since this field is 
of constant strength, no inductive action between the 
armature and field 1 can take place. Relatively to field 
2 the speed of the armature is 100 revolutions per second, 
and the inductive action between this field and the arma- 
ture will be precisely the same as if we had a true re- 
volving field of strength F = 50,000 and frequency 100 
acting on a stationary armature. Similarly, if we revolve 
the armature with a speed of 48, the relative speed to 
field 1 will be 2 per second, and that to field 2 98 per 
second. Now both fields act inductively on the armature, 
and the current flowing in any armature bar may be 
considered the resultant of two currents,, one induced by 
field 1 and the other by field 2. As far as each field and 
the armature currents induced by it are concerned, it is 
obvious that the machine may be regarded as a combi- 
nation of two rotary field motors running respectively at 



SINGLE PHASE MOTOR. 361 

the speeds of 2 and 98 revolutions per second, the fre- 
quency being 100 cycles per second. What is, however, 
not obvious at first sight is that we may determine the 
torque produced by each field, as if it were acting alone. 
In other words, are we justified in assuming that the 
armature current produced by field 1 is for the produc- 
tion of torque only acted upon by this field, and not also 
by field 2 ? The following consideration will show that 
this is, indeed, the case. The current induced by field 1 
in any armature bar has a frequency of 2, whilst the 
same armature bar cuts through field 2 with a frequency 
of 98, that is, at a frequency 49 times as great. Denote 
this ratio generally by m, then we have the instantaneous 
value of the force resulting from the interaction of field 2 
on the current produced in the armature bar by field 1 
given by an expression of the form 

K sin (m a) sin a 

where K is a constant, and the angle a refers to the 
slower of the two periods. To find the sustained 
mechanical effect we must integrate over a whole period 
or over several periods. The integration over one period 
gives 

" 2tt 
~ I K sin (m a) sin a d a 



-/. 



The value of this integral is 



~K 



sin (m— -1) a sin (m -f- 1) « 
2 (to— 1 ) "" 2 (to + 1) 



7T 



o 



o 

for all cases where mis a whole number. Thus for the 
case assumed, where m = 49, there is no mechanical effect 



362 ELECTRIC TRANSMISSION OF ENERGY. 

of one field on the armature current produced by the 
other field. The same would be the case if we revolved 
the armature of the motor with a speed of 46 revolutions, 
making the frequencies 4 and 96, or m = 24, whilst at 
the intermediate speed of 47 revolutions when the fre- 
quencies are 3 and 97, m is not a whole number, and the 
above expression has a certain, though obviously very 
small, value which may be either positive or negative. 
This refers, of course, to one period only, since we have 
extended the integration only over the time of one period. 
It is obviously permissible to extend the integration over 
two, three, or more periods, because the work stored in 
the revolving mass of the armature is immensely great in 
comparison with the small increment or decrement of 
work that is produced by this small force acting during 
several periods first in the direction of motion, and then 
during an equal number of periods in opposition to the 
motion. If, then, Ave extend the integration over a 
sufficient number of periods, the value of the integral is 
always zero. To get the actual torque at various speeds, 
we may, therefore, combine the two torque diagrams 
which would result from the consideration of each field 
by itself. Thus, let for instance in Fig. l\S A Y represent 
the torque diagram of field 1, revolving with a frequency 
of 100 in a clockwise direction relatively to the arma- 
ture. The length 0. 2 O x would then represent 100, and 
the relative speed of the armature would be measured to 
the left from 2 ; its absolute speed in space to the left 
from O. If the absolute speed of the armature is O s its 
speed relatively to field 1 is 0. 2 s, and the torque exerted 
on it by this field is given by the length of the line s T,. 
This torque is exerted in the sense in which the armature 
is rotating, and is therefore positive. The relative speed 



SINGLE PRASE MOTOR. 



363 



of the armature as regards field 2 is similarly 1 — s 
= s l9 and the torque produced by field 2 is given by 
the length of the line s T 2 . This is exerted in a direction 
opposed to the movement, and is therefore negative. 
The resultant torque is the difference between these two 
torques or 

s T= s T x — s T 2 . 

By determining this difference for various speeds O s we 
obtain the resultant torque curve A. It will be seen that 

Fig. 118. 




this curve passes through zero for speed zero, that is, 
when the armature is at rest ; and that it again passes 
through zero at a speed slightly short of synchronism. 
Between these two values the torque is positive, and has 
one maximum. The working is stable for armature 
speeds exceeding that which corresponds to maximum 
torque and unstable for lower speeds. The direction in 
which the motor runs is indifferent. We supposed the 
motor was started in a clockwise direction when its torque 
is given by the curve A. Had sve started it in a counter 
clockwise direction its torque would be represented by 



364 ELECTRIC TRANSMISSION OF ENERGY. 

the dotted curve A 1 symmetrically placed to the other 
side of 0. 

It is obviously of advantage to so design the motor that 
the ordinates of A shall be large, and this will be the case 
if the torque curve A Y rises high in its left branch and 
tails oft' low in its right branch. Now the condition for 
such a curve is that the motor shall have a sensible 
amount of self-induction. It is easily seen that a motor 
without self-induction, such as on page 328 was taken as 
a type of "perfect motor," could not possibly work on a 
single phase circuit. In such a motor (if it were possible 
to build it) the torque curve A l9 instead of being of the 
shape shown in Fig. 118, would be a straight line sloping 
from : upwards to the right, and A 2 would be a sym- 
metrical line sloping from 2 upwards to the left. The 
resultant torque curves would also be straight lines 
sloping downwards from O to the right and left, that is to 
say, having negative ordinates. Such a motor would 
therefore not only refuse to start by itself, but would also 
resist the motion impressed by an external source, the 
more, the faster it is driven. A motor of this kind (that 
is, one having no self-induction) would therefore be 
absolutely unworkable on a single phase circuit, though 
used as a true rotary field or multiphase motor it would 
be perfection. Such perfection is, of course, not attain- 
able in practice, and some self-induction must always be 
present ; but whereas in a multiphase motor self-induction 
is one of its objectionable features, it is an absolute 
necessity in a single phase motor. 

It was shown in the former chapter how the self- 
induction (or what comes to the same thing, the magnetic 
leakage) in a multiphase motor may be experimentally 
investigated, and some figures were given from tests made 



KOLBEN S EXPERIMENTS, 



365 



by Mr. Kolben with such a motor. The same motor was 
also tested for leakage when working on a single phase 
circuit by having all its thirty-six field coils connected in 
series. The total number of field turns is then 252, and 
the following results were obtained : 

Frequency, 50 ; E.M.F. on field, 180 ; current in field, 
18-8 ; watts absorbed, 432. The maximum E.M.F. in- 
duced in the experimental armature coil of 60 turns was 54 
volts when the armature was placed in certain positions 
relatively to the field coils ; in other positions the E.M.F. 
was smaller, varying down to zero. When plotted the 
E.M.F. curve was found to be almost exactly of sine 
shape, and the average E.M.F. may therefore be taken as 

252 34*4 
54/ — = 34*4. We find thus the leakage factor — — x — — 

= -800. 

Of every 1,000 lines passing through the field coils, 
200 are lost by leakage and 800 pass through the arma- 
ture when running light. When running under load the 
proportion passing through the armature would be still 
further reduced, as explained in the previous chapter. 
The following is a brake test made by Mr. Kolben on a 
3 H.P. Oerlikon single phase motor at 50 frequency, 
and the reader should compare these figures with those 
given previously for three-phase motors. It will be seen 
that the power factor is smaller and the slip greater. 



BH.P. 


B Watts. 


Field 
Current. 


Field 

Voltage. 


Apparent 
Watts. 


WaUs 1 Po ™ 
llpnt 8 , Factor ' 


Slip 
per 
cent. 


Efficiency 
per cent. 


3'6 



2,650 



45 
21-8 


110 
112 


4,950 
2,440 


3,766 
410 


76 

16'8 


4-5 




70*5 




In larger motors the power factor may reach or even 



366 



ELECTRIC TRANS3IISSI0N OF ENERGY. 



exceed 90 per cent., as will be seen from the following 
table giving results of four tests made by Riccardo Arno * 
on a 15 H.P. Brown single phase motor. This motor is 
remarkable in so far as it has no sliding contacts whatever. 
The resistance of the armature winding is therefore not 
artificially increased during the period of starting, and a 
correspondingly large current is taken at starting, as 
will be seen from the first line in the table. The 
means employed for making such motors self-starting are 
explained later on. The motor in question is built for a 
frequency of 40 cycles per second, and having a six pole 
winding on the field, its speed should be slightly under 
800 revolutions per minute. During the test the frequency 
of the supply current was, however, over 40, which accounts 
for the speed, even under load, exceeding 800 revolutions. 
The supply pressure is 150 volts. During the test the 
motor was loaded by a brake and all the electrical read- 
ings were taken with carefully calibrated instruments. 





Test of 


15 H.P. 


Sing I 


e Phase Brown Motor. 


Speed. 


Watts on 
brake. 


True 

Watts 

supplied. 


Volts. 


Amperes. 


Apparent 

Watts. 


Power 

Factor 
per 
cent. 


Efficiency 
per cent. 








17,595 


132 


150 


19,800 


89 





876 





688 


157 


27 


4,252 


16 





862 


574 


1,173 


156 


27 


4,303 


27 


49 


863 


1,943 


2,652 


155 


31 


4,774 


56 


73 


866 


2,870 


3,774 


157 


36 


5,630 


67 


76 


868 


4,136 


5,176 


156 


42 


6,520 


79 


80 


863 


5,085 


6,171 


154 


47 


7,307 


84 


82 


862 


5,652 


6,732 


154 


51 


7,792 


86 


84 


859 


6,940 


7,854 


152 


57 


8,694 


90 


88 


858 


7,728 


8,823 


151 


64 


9,634 


92 


88 


856 


9,980 


11,398 


149 


82 


12,218 


93 


88 


851 


11,385 


13,923 


146 


102 


14,943 


93 


82 


812 


11,886 


15,478 


143 


118 


16,903 


92 


77 


816 


12,320 


16,626 


144 


128 


18,432 


90 


74 



1 " L'Elettricista," III. No. 7, p. 149, 



STARTING DEVICES. 367 

The working of single phase motors has been already 
explained both in a general way, and more particularly 
by reference to the torque diagram. It, however, remains 
yet to explain how such motors are started. In small 
sizes a vigorous pull on the belt by hand is generally 
sufficient to give the armature a speed sufficiently high 
to make the corresponding torque exceed the friction al 
resistance of running light, and a small motor may 
thus be started by hand, if there is a fast and loose 
pulley provided on the shaft which receives the power 
from the motor. Larger motors are, however, too heavy 
to be started in this way, and some special starting 
appliance is necessary. A variety of such appliances 
have been designed, but they all depend upon the expe- 
dient of splitting up the single phase current brought by 
the supply leads into two components of different phase. 
The field of the motor is wound with two sets of coils, 
and these are connected with the two branch circuits in 
such a way as would produce a true rotary field if the 
phase difference between the branches were 90°. If the 
phase difference has a smaller value, the resultant field 
will still be rotary, although it will not be of constant 
strength, but such as it is, it suffices to start the motor, 
and after a certain speed has been attained the starting 
appliance is cut out, and the connections with the field 
coils are altered, so as to form one circuit only, produc- 
ing an oscillating field. The motor then runs quickly up 
to a speed near synchronism, after which the load may be 
thrown on. The difference in phase between the two 
components of the supply current may be produced by 
inserting ohmic resistance into one branch, and in- 
ductance into the other ; or inductance and capacity, or 
only capacity into one branch, the natural inductance of 



368 



ELECTRIC TRANSMISSION OF ENERGY. 



the field coils in the other branch being sufficient to pro- 
duce a sensible phase difference. This is the arrange- 




Rest 




Stewfisng 




Full Speed 



ment adopted by Mr. C. E. L. Brown, and which is 
shown diagramatically in Fig. 119. The condenser used 
by Mr. Brown is of the liquid type, and has an enormous 



brown's starting gear. 369 

capacity ; the pressure between any two neighbouring 
plates must, however, not be too high, hence a number 
of dish-shaped plates are put in series, and the first and 
last plates are connected to the circuit. The current 
at starting being in any case large, whilst the E.M.F. 
required is small, Mr. Brown combines with his con- 
denser a transformer, so that whilst the line is only called 
upon to give a moderate current at full voltage, the 
motor receives a large current at reduced voltage. The 
necessary changes in the connections from " rest " to 
"starting" and "full speed," are performed by one 
switch, as will be seen from the three diagrams in fig. 
119. M is the motor, C the condenser, and S the switch. 
The leads on the right bring in the supply current ; the 
other leads serve as connections between the motor and 
its starting device. The winding of the motor consists 
of two coils, a and b ; the latter is merely an auxiliary 
coil of finer wire than coil a; and it is only in use 
during the period of starting, when it is put in series 
with the condenser. The current in it is in advance over 
the current a by in something less than a quarter period, 
thus producing a rotary field. The switch at starting is 
thrown over to the left. When the switch is thrown 
over to the right the main coil a is coupled directly in 
parallel with the supply leads, and the auxiliary coil b 
and the whole starting device is completely cut out of 
circuit. 



B B 



CHAPTER XI. 

The Line — Relation between Capital Outlay and Waste of Energy — Most 
Economical Method of Working — Weight of Copper in relation to Power, 
Distance, Voltage and Efficiency — Phase Rectifier — Weight of Copper 
required with Different Systems of Transmission — Material of Conductor 
— Stress in Conductor — Insulators — Joints — Lightning Guards. 

Both as regards first cost and economy of working, the 
line forms a very important item in any extended system 
of electric transmission of energy. We have to consider 
two separate cases. The one, where energy from a 
central station is transmitted to and divided between a 
number of small working centres all grafted upon a net- 
work of conductors forming the main circuit, and the 
other, where all the energy is conveyed to a single 
receiving station along a pair of conductors without any 
ramifications. The first case would occur in a system of 
town supply where electricity is furnished for lighting 
and power purposes, and where the lamps and motors 
are all connected in parallel to the mains. The second 
is that occurring when energy from an hitherto inaccessible 
source is conveyed to a convenient point of application, 
the distance being considerable. Whatever particular 
form of transmission and distribution the system may 
have, it will be clear that the first cost of the conductors, 
and the annual expenditure represented by the energy 
wasted in heating the conductors, follow opposite laws. 
To economize energy it is necessary to employ leads of 



LORD KELVIN'S LAW. 371 

low resistance, and, therefore, of considerable cross-sec- 
tional area. To reduce the first cost we would, on the 
other hand, employ leads of small weight — that is, of 
small sectional area. We see that first cost and the 
subsequent working expenses are both governed by the 
area of conductor chosen, but whilst the former increases 
with the area, the latter decreases as the area increases, 
and it is evident that in each system of electric trans- 
mission of energy there must exist at least one particular 
area of conductor for which the sum of interest on its 
first cost, and annual cost of energy wasted, becomes a 
minimum. The subject is very complicated as elements 
enter into the calculation which cannot well be brought 
into mathematical form. To simplify the problem we at 
first shall neglect all these bye-issues, and treat the 
question in a purely academical way ; we shall then 
extend the theory to practical cases. 

The items which more especially affect the most 
economical size of conductor are : 1. The rate of interest 
to be charged on capital outlay ; 2. The cost of one 
horse-power-hour at the terminals of the generator ; 
3. The number of hours per annum that the energy is 
required; 4. The cost of unit weight of the conduct- 
ing material ; 5. The cost of insulation ; 6. The cost 
of supports if an overhead line, or troughs if an un- 
derground line ; 7. The cost of labour in laying. If 
it be permissible to consider the capital outlay as pro- 
portional to the total weight of conducting material, 
then for a given line we have the relation p K = k a p, 
where K is the total cost of the line, k a constant and p 
the annual rate of interest. The resistance of the line is 
inversely proportional to the area a, and the energy 
wasted equals resistance multiplied by the square of the 



372 ELECTRIC TRANSMISSION OF ENERGY. 

current. Let q represent the cost of one electrical horse- 
power-hour at the terminals of the dynamo, and let t 
represent the number of hours per annum during which 
the current c is flowing — there being always the full 
amount of energy transmitted — then we have the annual 
value of energy wasted, 

TIT W 1 

W= - q t c 2 

w being a constant. The total expenditure will be a 

.^dKp-dW 

minimum it ; — I — -, — = o. 

da da 



This gives p K= W -^ — , and 



V v k 



a 

V 



By inserting this value into the equations for K and W 
we find 



p K= c v w q t k p and 
W— c v w q t k p 
Hence p K= W^ 

or the most economical area of conductor, will be that for 
which the annual interest on capital outlay equals the 
annual cost of energy wasted. This law is commonly 
known as Lord Kelvin's law, and was first pub- 
lished by him in a paper on " The Economy of Metal 
Conductors of Electricity," read before the British Asso- 
ciation in 1881. It should be remembered that this 
law in the form here given only applies to cases where 
the capital outlay is strictly proportional to the weight 
of metal contained in the conductor. In practice this is, 
however, seldom correct. If we have an underground 
cable, the cost of digging the trench and filling in again 



lord kelvin's law. 373 

will be the same whether the cross-sectional area of the 
cable be one tenth of a square inch or one square inch ; 
and other items, such as insulating material, are if not 
quite independent of the area, at least dependent in a 
lesser degree than assumed in the formula. In an over- 
head line we may vary the thickness of the wire within 
fairly wide limits without having to alter the number of 
supports, and thus there is here also a certain portion of 
the capital outlay which does not depend on the area of 
the conductor. It would, therefore, be more correct to 

write 

K=Ko + ka, 

where Ko represents that part of the capital outlay which 
is constant and independent of the area of the conductor. 
This addition on the right-hand side of the formula 
makes no alteration in the differential equation, for 

dKo 

1 = - 

a a 

We obtain, therefore, again, 



pk ' 

but the value of p K is altered. 

p K—p Ko-^-cVwqtkp 

W = */ w q t k p. 

The interest on capital outlay, and the annual cost of 
energy wasted are now in the relation 

p K=p Ko +■ W. 

They are no longer equal, but the interest on capital out- 
lay must be greater than the annual cost of energy wasted. 
By writing the above equation in the form 

p (K-Ko)=W, 



374 ELECTRIC TRANSMISSION OF ENERGY. 

we find that the most economical area of conductor is that 
for which the annual cost of energy wasted is equal to the 
annual interest on that portion of the capital outlay which 
can be considered to be proportional to the weight of 
metal used. 

Up to this point we have treated the subject in what 
was at the beginning of this chapter called the purely 
academical sense. Let us now see how the result 
can be practically applied. That the deduction here 
arrived at is not directly applicable to a transmission 
plant is obvious, because certain important premisses 
have been disregarded. To see clearly that the law of 
maximum economy indiscriminately applied may lead 
to a wrong conclusion, we need only remember that 
according to this law the sectional area of the conductor 
is proportional to the current and does not depend on the 
voltage of the generator or the distance of transmission. 
If the law as above enunciated were universally applicable 
it would also have to fit a case where the voltage is low 
and the distance great ; and under such circumstances it 
is quite conceivable that the whole of the available vol- 
tage is required for overcoming the ohmic resistance of 
the line and that no power at all is delivered at the motor 
end. The law would thus seem to indicate that the most 
economical method of working a line of transmission is 
one under which we get no return at the motor end for 
our annual outlay at the generator end, which is obviously 
absurd. The fallacy does not, however, lie in the law, 
but in our application of it. The law itself is perfectly 
true. It says that if a certain current has to be sent 
through a given circuit, then there is one particular area 
of cross-section for which the annual outlay of sending the 
current round becomes a minimum. The fallacy lies in 



LORD KELVIN'S LAW EXTENDED. 375 

this, that we assume the earning power at the motor end 
of the circuit to become a maximum when the cost of 
sending the current through the circuit becomes a mini- 
mum. This is not the case. The law also assumes that 
the power has the same money value all along the line. 
This can obviously not be the case, for if the annual 
horse-power could be produced locally at the motor end 
as cheaply as it can be produced at the generator end, 
then there would be no need at all for a transmission 
plant. Further, the law assumes that the electrical horse- 
power has a certain annual value quite irrespective of the 
voltage at which the current is delivered. This, again, is 
not correct. Generators for a very high voltage cost 
more to build and maintain than generators for a mode- 
rate voltage. It is thus obvious that the voltage at which 
the plant is intended to be worked must be taken into 
account in designing the line for greatest economy. We 
must further take into account not only the interest and 
depreciation of the line, but also the interest and depre- 
ciation of the machinery at either end. The whole 
problem is exceedingly complicated and cannot be solved 
by reference to the line only ; the investigation must 
extend over the whole of the plant. 

In order to present the problem in the simplest possible 
form we assume that the transmission of power is to be 
effected by continuous current. The transition to alter- 
nating and polyphase currents can then be made by 
establishing the relations existing between the weight of 
copper required with continuous currents and other 
systems of transmission. The conditions under which the 
problem is generally met with in practice are the follow- 
ing. The maximum voltage at generator terminals is 
either given or may be selected with due regard to con- 



376 ELECTRIC TRANSMISSION OF ENERGY. 

structive reasons and local conditions. It is generally 
found that the economy in working is greatly influenced 
by the voltage, and for this reason alternative designs at 
various voltages should be prepared so that the best may 
be finally selected. The annual value of the brake H.P. 
at the generating station is known, as is also the brake 
H.P. required at the motor end, distance of transmission 
and cost of machinery and regulating appliances per H.P. 
Having decided on the type of line to be employed, we 
also know the cost of supports for the conductor per mile 
and the cost of the conductor itself per ton of copper 
erected. The data required are area of conductor, 
working current, power required at generating station, 
total efficiency, total outlay, and total annual cost per 
brake H.P. delivered. The latter to be a minimum. 

We assume the efficiency of the generator and motor 
to be 90 per cent, for each ; and the resistance of the 
line to be -088 ohm for one square inch of conductor for 
one mile out and home. Assume the following notations : 

D Distance in miles. 

a Section of conductor in square inches. 

E Terminal volts at generator. 

e Terminal volts at motor. 

HP^ Brake horse-power required to drive generator. 

HP m Brake horse-power obtained from motor. 

c . Current in amperes. 

Efficiency of generator 90 per cent. ; efficiency of motor 
90 per cent. 

g Cost in £ per electrical horse -power output of generator. 

m Cost in £ per brake horse-power output of motor in- 
cluding regulating gear. 

G = '9g HPg . . Cost in £ of generator. 

M = m HP m . . Cost in £ of motor and regulating gear. 

t = 18*2 Da . . Weight in tons of copper in line. 

K Cost in £ per ton of copper, including labour in erection. 

s Cost in £ of supports of line per mile run. 

p Cost in £ of one annual brake horse-power absorbed 

by generator. 

q Per-centage for interest and depreciation on the whole 

plant. 



lord kelvin's law extended. 377 

The power delivered to the motor is 830 H P m watts ; 
and that wasted in the line is E c — 830 H P m watts. This 
must obviously be equal to resistance of line multiplied 
by the square of the current. 

E c - 830 HP m = -088 - c\ 
m a 

The sectional area of conductor is from this equation. 

'088 D c 2 
a ~Ec-830HE m ' 

The capital outlay for the conductor and erection irre- 
spective of supports is 

tK=l82DaK, 

and by inserting the value for a we have 

Cost of conductor = ^^p- 

The total capital outlay on which interest and deprecia- 
tion has to be charged consists of this item plus the cost 
of supports D s ; plus cost of machinery at the motor end, 
m H P m \ plus cost of machinery at the generator end, 

E c 

g YTn- W e thus obtain the capital outlay, 

Annual cost per brake horse-power delivered = q jj— + 

p hp: 

830 
y = —=rHP m , the current which would be required if the 

line had no resistance ; 



378 ELECTRIC TRANSMISSION OF ENERGY. 

E B 

and /3 = 7 2 — — ; then the most economical 

1*6 q K D + E B 

current at the given voltage E is 



= y(l + jl-l 2 ) 



c = y(l+ / V6 * K & V 
V Vv&qKD+BEJ 

Having found the current c, we can from e 1 c = 830 
H P m calculate the voltage e 1 at the motor end of the 
line and thus find E—e 1 , the voltage lost in line resis- 
tance. The line resistance itself and therefore the section 
and weight of line can now also be found as well as all 
the other data required, including the total annual cost 
per H.P. delivered. By making the calculation for 
several values of E 9 due account being taken of the 
influence of voltage on the cost of machinery and insula- 
tion of the line, it will be found that the cost per H.P. 
delivered varies with the voltage, and that there is for 
every case one particular voltage at which the plant will 
work with the greatest economy. Provided local con- 
ditions permit it, this voltage should be chosen. It is 
interesting to note that the square root in the equation 
for the current can never be greater than unity. It 
approaches unity the more nearly the smaller the voltage, 
and the greater the distance of transmission. For econo- 
mical working we would thus always find 

c<2y. 

If c were equal to 2 y, then half the total power would be 
lost in the line, but since c must be smaller it follows that 
under no circumstances can it be economical to lose as 
much as half the power in the line. Apart from econo- 
mical reasons the loss of power in the line is with alter- 



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380 ELECTRIC TRANSMISSION OF ENERGY. 

nating currents further restricted by the necessity of 
providing a sufficient margin of power as already 
explained in Chapter VIII. 

For preliminary or approximate calculations as to the 
weight of copper required for any line, it is convenient 
to use tables or diagrams which can be prepared once for 
all. Fig. 120 shows a set of such diagrams for continuous 
current power transmission at 1 5 000, 2,000, 5,000 and 
10,000 volts. Although continuous currents would not 
be used at a pressure of 10,000 volts, it is convenient 
to make the continuous current transmission the standard 
as regards weight of copper to which other systems may 
be referred, as will be explained later on. In all the 
four diagrams Fig. 120 distance of transmission is plotted 
on the horizontal, and weight of copper given in tons on 
the vertical. The motor is supposed to have an efficiency 
of 91 per cent., and the power actually delivered at the 
motor spindle is supposedtobe 100 brake horse-power. For 
a larger or a smaller power the weight of copper scaled off 
the diagrams would have to be proportionately altered. 
The voltage written in each diagram is that measured at 
the terminals of the generator, that is to say, the highest 
voltage on the line. The length of conductor is taken at 
5,400 feet (not 5,280 feet) per mile to allow for the sag of 
the wire between the posts. Each diagram contains 4 
curves, marked respectively >i = # 6 ; n = -7 ; n = # 8; 
n = *9. This means that the efficiency of the line itself 
is respectively 60, 70, 80, and 90 per cent. The use of 
these diagrams is very simple, and may be explained by 
an example. Say we have to transmit power over 20 
miles, and wish to do so with a line efficiency of 80 per 
cent., and a pressure of 5,000 volts on the terminals of 
the generator. We find from the diagram that for every 



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382 



ELECTRIC TRANSMISSION OF ENERGY. 



100 brake horse-power delivered we would require 13^ 
tons of copper in the line. 

Fig. 121 gives similar diagrams in a different form. 
The volts are plotted horizontally and tons of copper 
vertically, whilst the curves refer respectively to 1,2, 5, 
10, 15, and 20 miles of distance over which the power 
has to be transmitted. Given voltage, distance and 

Fig. 122. 



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efficiency, the copper weight can be scaled off the diagram. 
Fig. 122 shows the relation between efficiency and copper 
weight for various distances, but in all cases for the same 
pressure, namely, 5,000 volts. For instance, a 90 per 
cent, efficiency line 25 miles long contains 37 tons of 
copper for every 100 horse-power delivered. If we are 
satisfied with 80 per cent, efficiency the weight is only 
20 tons, at 70 per cent, only 16 tons, and so on, the 



WEIGHT OF COPPER IN LINE. 383 

lowest weight being reached at 50 per cent, efficiency. 
For a less efficiency than 50 per cent, the weight increases 
again, so that on account of prime cost in copper it would 
obviously be wrong to make the line efficiency less than 
50 per cent. This result is in accordance with that found 
a few pages back when we deduced from c < 2 y that 
under no circumstances can it be economical to lose 
more, or even as much as half the power, in the line. 

When comparing different systems of transmission as 
regards weight of copper in the line, we must first of all 
agree on a suitable standard of comparison. That the 
comparison can only be fair if we take the same power 
delivered, the same distance and the same efficiency, will 
be obvious. The only other condition affecting weight is 
the voltage, and this must, therefore, be our standard of 
comparison. The question now arises as to the exact 
meaning of the term voltage in this connection. In a 
continuous current transmission the meaning is perfectly 
definite, but with alternating currents there is a doubt 
whether we ought to take effective volts, or the volts 
corresponding to the crest of the pressure wave. If the 
question were merely one of using machines as put on 
the market by various makers, then effective volts would 
have to be taken, because the machines are designed and 
listed to work at pressures given in effective volts, and 
their insulations may be assumed to be sufficient for their 
pressures. In this case a 2,000 volt alternating current 
transmission would require the same weight of copper 
in the line, as a 2,000 volt continuous current trans- 
mission provided, in the former case there is no lag 
between E.M.F. and current, and that the current and 
E.M.F. waves are sinusoidal. But this is not the correct 
way of considering the question. The limiting condition 



384 ELECTRIC TRANSMISSION OF ENERGY. 

is not the difficulty of designing a winding that will give 
a high voltage, but the difficulty of effectually insulating 
that winding so that it will safely stand the high voltage. 
In other words, the stress on the insulation and not the 
effective voltage is the factor which must be taken into 
consideration, and which must form the basis on which 
different systems of power transmission must be com- 
pared. Thus an alternator which gives a very peaky 
E.M.F. curve when working at 1,000 volts effective 
pressure, may strain its insulation as much or more than 
another alternator giving a sine curve, and working at 
2,000 volts effective pressure. Obviously the line, if 
supplied from the first machine, would require to be four 
times as heavy as if supplied from the second machine, 
and it will thus be seen that with regard to safety it is 
advantageous to employ machines which give an E.M.F. 
curve of sinusoidal shape. Let us then assume that 
single and multiphase alternators are all so designed as to 
give true sine curves and let us compare the following 
systems with a continuous current plant : a) Simple 
alternating ; b) two-phase alternating with two indepen- 
dent circuits requiring four wires ; c) two- phase alterna- 
ting with one wire common to both phases, and requiring 
therefore only three wires ; and d) three-phase alterna- 
ting with three wires. We also assume for the sake of 
simplicity that in neither case is there any lag between 
E.M.F. and current. As a rule there is lag, and the 
effect of this is that the current must be larger than 
would otherwise be the case, so that the weight of copper 
will be increased in the ratio of 1 to cos ^. In a single 
phase transmission the lag may be avoided by suitably 
exciting the motor as explained on page 261. In a multi- 
phase transmission the same expedient is not applicable ; 



PHASE RECTIFIER. 



385 



but we may use another expedient to reduce the lag in 
the line to zero. This is the invention of Von Dobro- 
wolsky, and consists in the addition of an idle running 
alternator to the receiving plant at the motor end of the 
line. 

Such a machine might appropriately be called a 
u phase-rectifier/' and its armature must be wound for 
two or three circuits according to the number of phases 
produced by the generator. To explain the principle on 

Fig. 123. 




which the action of the phase-rectifier depends, we must 
go back to Fig. 114, where O E represents the impressed 
E.M.F. (that is, in the case of a transmission plant the 
E.M.F. at which the current enters the motor), and O C 
the current. The diagram refers, of course, only to one 
of the phases. It will be seen that under no circum- 
stances can the angle of lag <p become zero, although in 
practical work it is generally much smaller than was 
shown for the sake of clearness in the diagram. The 
lines O C and O E are reproduced in Fig. 123. The 

C C 



386 ELECTRIC TRANSMISSION OF ENERGY. 

length of the line C may be taken to represent the 
current flowing through the cable (or in a three-phase 
plant through one of the three conductors of which the 
cable is composed), whilst the current doing useful work 
is smaller, namely O 7, which is the projection of O C 
on the E.M.F. line. The problem now is to reduce the 
line-current without altering the working conditions of 
the motor, and this problem Von Dobrowolsky has solved 
by coupling in parallel with the motor an alternator ex- 
cited so as to give a higher E.M.F. than that of the 
supply current. Such an alternator, if running light, 
will take a leading instead of a lagging current, and by 
suitably designing the plant, it is possible to so arrange 
matters that the lead of the current taken by the phase- 
rectifier exactly compensates for the lag of the current 
taken by the motor, so that the resultant current flows 
through the line without lead or lag. In the diagram 
the length of E K 2 is the E.M.F. of the phase-rectifier, 
which combined with the supply E.M.F. O E 3 gives the 
resultant E.M.F. O E 2 . To this resultant E.M.F. 
corresponds the current O I l9 taken by the phase-rectifier. 
The resultant between this current and the current taken 
by the motor is O Y~ 2 , and this is the current which 
actually flows through the line. It is made up of two 
components ; the one, O 7, which is the true power current 
of the motor, and the other 1 1 2 , which is the power cur- 
rent required to keep the phase-rectifier in motion. The 
latter is of course exceedingly small, amounting to some 
two or three per cent, of the motor-current only ; in the 
diagram it has, however, been shown large in order to 
make the construction clear. In practice there is no 
need to make any elaborate calculations as to the exact 
E.M.F, to which the rectifier should be excited. All 



COPPER WEIGHT WITH DIFFERENT SYSTEMS. 387 

we need do is to provide a rheostat by which the excita- 
tion can be varied, and to turn its handle into that posi- 
tion for which the amperemeter in the supply circuit in- 
dicates minimum current. Either more or less excitation 
will result in an increase of supply current, and we thus 
know that for that particular excitation, and at the given 
load on the motor, we have coincidence in phase of cur- 
rent and E.M.F. in the line. The rectifier may be 
excited by a little dynamo on its own shaft, and may be 
started by the motor by means of a friction-clutch or 
other mechanical device capable of being disconnected 
after synchronism is reached. 

After this digression, intended to show how alternating 
current lines may be worked without lag, we return to 
the main problem, which is the comparison of the five 
systems of transmission above enumerated. Taking the 
continuous current system as our standard of comparison, 
and putting the condition that the factor of safety against 
a breakdown of insulation shall be equal in all the sys- 
tems, we can express the amount of copper required for 
each system in terms of the amount required by the con- 
tinuous current system. The conditions of equal safety 
requires that at no moment shall the E.M.F. between any 
two-line wires, or between any line wire and earth, exceed 
the corresponding values obtaining in the continuous 
current plant. 

Take the single phase alternating current first. The 
power transmitted is proportional to the effective E.M.F., 
the stress on the insulation to the maximum E.M.F. 
The latter must be equal to the E.M.F. of the continuous 
current. The effective E.M.F. of system a) is thus only 
1/ ^2, of that of the standard system, and as the 
copper weight varies inversely with the square of the 



388 ELECTRIC TRANSMISSION OF ENERGY. 

E.M.F., the ratio of copper weights is 1/2, that is to say, 
the alternating current requires twice as much copper as 
the continuous current. 

The two-phase system with four-line wires being simply 
a duplication of the previous case, the same relation holds 
good. 

The two-phase system with three-line wires might, at 
first sight, appear to result in a saving of copper because 
the common wire carries not twice, but */2 times the 
current carried by each of the two other wires. This 
is, however, a fallacy. By joining two of the wires into 
one, we have forcibly raised the potential difference 
between the two other wires to v 2 times the previous 
amount ; and to get back to our original conditions of 
safety we must correspondingly lower the E.M.F. in 
each circuit. This results in a considerable increase of 
copper in the line. It is not necessary to give the calcu- 
lation in detail ; the result is that this system requires 2*9 
times the standard weight of copper. 

In a three-phase system with star-coupling, the maxi- 
mum potential difference between any two wires is ob- 

viously 2 */E 2 —~t = E v 3, when E is the maximum 

E.M.F. in one phase. The equivalent continuous cur- 
rent system would therefore be worked at a pressure of 
E v^3, and if the current be C, the power put into the 
line is C E \/3. Let i be the alternating current in 
each phase, then the power put into the line is 3 i E/\^2 9 

from which we find i = C ^ Let R and r be the re- 
sistance of one-line wire in the continuous and alternat- 
ing system respectively, then for equal loss we have 
2 R C 2 = 3 r i 2 , and since from the above equation for i, 



COPPER WEIGHT WITH DIFFERENT SYSTEMS. 389 

3 i 2 = 2 C 2 , it follows that i? = r, that is to say, a wire 
of the same section must be used in both systems. Since 
there are three wires in the alternating and only two in 
the continuous current system, the weight of copper is as 3 
to 2, or 1*5 to 1. For a three-phase plant with link 
coupling, a similar investigation leads to the same con- 
clusion. Summarizing these results, and assuming as a 
basis that 10 tons of copper are required with the con- 
tinuous current system, we require for an equal factor of 
safety, against breakdown of insulation : 

tons. 

a) with siDgle phase alternating current . . 20 

b) with two-phase alternating current and four 

wires . 20 

c) with two-phase alternating current and three 

wires 29 

d) with three-phase current and three wires . 15 

The three-phase system thus has an appreciable advan- 
tage, in so far as the weight of copper in the line is con- 
cerned. It must be remembered that the comparison 
with the continuous current system has been made 
merely with a view to adopt a convenient standard. In 
practice it is of course not possible to work a continuous 
current system at so high a pressure as any alternating 
current system, as already explained in a former chapter, 
and where the distance is great, the adoption of alternat- 
ing current in preference to continuous current must 
always result in a saving of copper for the line. 

The question whether the line should be carried over- 
head or placed underground, depends on a number of 
local circumstances. In many cases, and especially for 
distribution of power within populous districts, an under- 
ground system is the only admissible one, and then any 



390 ELECTRIC TRANSMISSION OF ENERGY. 

types of high pressure cable which have stood the test 
of practical experience in lighting may be used. It may 
also happen that although no objection exists on the part 
of public authorities to an overhead line, yet the under- 
ground line is preferable on account of climatic condi- 
tions. In districts where the winter is very severe, or 
where during the summer thunderstorms are both fre- 
quent and violent, the upkeep of an overhead line is 
necessarily costly, and in such cases it may be good 
policy to adopt that system which is not so liable 
to interruption, although it may be the more expensive 
at the first start. Apart from such special cases, however, 
the overhead line, consisting of posts, insulators, and 
naked wires, is the one more generally used for power 
transmission, especially for long distances. 

The material used for the conductor is generally hard- 
drawn copper, but silicon bronze and phosphor bronze are 
also used. The properties required in the metal are 
great strength and high conductivity, conditions which 
to a certain extent are contradictory. Thus pure, soft 
copper has the highest conductivity, namely 100, but its 
breaking strength is only 16 or 17 tons per square 
inch. In hard-drawn copper the conductivity is only 
97 per cent., but the tenacity is 29 tons, whilst phosphor 
bronze of 45 tons has a conductivity of only 26 per cent. 
The following table gives the tenacity and conductivity 
for different materials : 



MATERIAL FOR LINE CONSTRUCTION. 



391 



Material. 


Tenacity. 

Tons per 

square inch. 


Conductivity. 


Soft copper, pure .... 
Hard- drawn copper . . . 
Silicon bronze 

>9 i!) .... 
53 J> .... 

Phosphor bronze . . . 
Cast steel 




16 

29 
28 
35 
48 
45 
59 


100 
97 
97 
80 
45 
26 
10 



The line taken by a wire between two supports is a 
catenary, but as the sag is always small, and as the sup- 
ports are generally at equal heights, we may without 
great error substitute a parabola. In this case the 
tangent of the angle with the horizontal at which the 
wire leaves the support is given by the ratio of twice the 
sag divided by half the span, and this is obviously also 
the ratio between the vertical and horizontal forces of the 
support. The vertical force is the weight of half the 
span, and the horizontal force (which without great error 
we may consider as equal to the stress or tension in the 

wire) is therefore 

W S 



T= 



8 s 



where JVi& the weight of wire in one span, S is the span, 
and s the sag. If a be the area of the wire in square 
inches, the weight per foot is 3*85 a lbs., and ^=3*85 a 5, 
which substituted in the equation for T gives 



T= -48 a (-) S. 



The stress per square inch of section is 

• = -* 8 (?) s 



392 ELECTRIC TRANSMISSION OF ENERGY. 

for a wire of hard-drawn copper, and as the density of 
the various bronzes is about the same as that of copper, 
the formula may be used also for wires of silicon or 
phosphor bronze. Thus a wire sagging 4 feet in a 
200 feet span would be subjected to a tensile stress of 
•48 x 5 x 200 = 4,800 lbs., or 2*15 tons per square inch. 
If the dead weight were the only force to be considered, 
such a wire of hard-drawn copper would have a factor of 
safety of 29/2*15 = 13*5. There are, however, other 
forces to consider, namely, wind pressure, accumulations 
of snow and ice, and influence of temperature. The 
latter, if not duly allowed for at the time the line is 
erected, may cause a considerable addition to the calcu- 
lated stress. The effect of cold weather is to cause the 
wire to shorten, thus reducing the sag and increasing the 
stress <t. Let L be the length of wire in one span, then 
from the theory of the parabola we have 

s=J\s{L-S\ 

which inserted into the above expression for a gives 

cr = -785 £#/ \/ L-S. 

This expression shows that the stress is increased if L 
becomes lessened, owing to a reduction of the tempera- 
ture. The temperature co-efficient of copper for expansion 
may be taken as '00172, so that the variation in L with a 
temperature variation of t centigrade is A L= *00172 t L. 
If we know the summer and winter temperatures, we 
can find the two extreme values for L and the two 
extreme values for the sag and stress from the condition 
of the line at the time of its erection ; or conversely, we 
can so settle these conditions when erecting the line that 



OIL INSULATOR. 



393 



the greatest possible stress in winter shall still leave a 
sufficient factor of safety. 

The posts, insulators, method of erection, use of guards, 
brackets, etc., are all similar to telegraph practice, 
though the work is generally of a heavier character and 
a higher degree of insulation is required. This is gene- 
rally obtained by means of the Johnson and Phillips's oil 

Fig. 124. 




insulator, which makes surface leakage impossible. 
Many forms of these insulators are in use, but the one 
illustrated in Fig. 124 may serve to show the principle. 
The insulator has an internal and external bell, and the 
former dips into an annular trough of china, which can 
slide on the stalk of the insulator, and is secured in its 
higher position by a pin as shown. The trough is filled 
with oil, and this cuts off completely any surface leakage 



394 



ELECTRIC TRANSMISSION OF ENERGY. 



that might otherwise take place. For cleansing and 
refilling with oil the inner trough is lowered. 

All insulators before being put up should be tested to 
make sure that the glazing is perfect, and that there are no 
cracks through the material which might allow electrical 
leakage to take place. To test an insulator it is 
placed upside down, the inner space is filled with acidu- 
lated water, and it is then immersed to near the rim in a 
bath of acidulated water. If the insulation is perfect, 
it must be impossible to pass even the most minute 
current measurable on a delicate galvanometer from the 

Fig. 125. 





liquid on the inside through the insulator to the liquid on 
the outside. 

The wire may be attached to the insulator either on 
the groove at the top or at the side, the latter if there 
should be a bend in the line occasioning a considerable 
lateral strain. The method of attachment in both cases 
will be seen from Figs. 125 and 126, where the views 
a, b, c, d and a b c, represent respectively the different 
stages of the process. 

Since wire and cables can only be obtained and carried 
to the place of erection in limited lengths, it is frequently 
necessary to make joints. A joint should not only be as 
strong as the wire or cable itself, but it must have an 



WIRE JOINTS. 



395 



absolutely perfect contact, as otherwise the passage of 
the current would heat and ultimately destroy it. It is 
also desirable to avoid the use of other metals than that 
of the conductor, so as to prevent electrolytic action. 
The use of solder is, for many joints, a necessity, and must 

Fig. 126. 






be exempt from this rule ; but it is not advisable to use 
iron couplings for a line of copper^ or any other combina- 
tion of two different metals. With thin wires a strong 



Fig. 127. 



joint is made, as shown in Fig. 127, which explains itself. 
To improve the contact, the middle portion is soldered 
over. Fig. 128 shows another form of joint suitable for 

Fig. 128. 




thin wires, which can easily be bent. A x A is one wire, 
B x B the other ; the ends A and B x are left long enough 
to allow of being lapped round the middle portion of the 
joint until they meet, and are then twisted together, as 
shown in Fig. 129. 

If the wire is too thick to allow of its being easily 



396 



ELECTRIC TRANSMISSION OF ENERGY. 



twisted into a knot, the joint shown in Fig. 130 is some- 
times used. The two ends of the wire are bent short at 
right angles, and placed side by side, so that the ends 
point outwards. In this position they are held by a 

Fig. 129. 




clamp whilst being served with a layer of binding wire 
of the same material as the conductor. When the space 
between the two ends is completely filled by the binding 
wire it is soldered over. 

Cables may be joined either by careful splicing or by 

Fig. 130. 




couplings. A very neat coupling has lately been intro- 
duced by Mr. Lazare Weiller ; it consists of a double 
hollow cone (Fig. 131) with an opening in the middle. 
The end of the cable is inserted at one end, brought out 
at the central opening, then doubled over and pushed 

Fig. 131. 




back again through the opening. A pull is applied to 
the cable as if to draw it out of the coupling, and this 
has the effect of jamming the end of the cable tightly in 
the cone. The end of the second cable is treated in the 
same manner, and to secure perfect contact, and prevent 



WIRE JOINTS. 



397 



any slipping back, melted solder is poured into the central 
opening. Fig. 132 shows the coupling in section and the 

Fig. 132. 



cables in place. As a suitable composition for the solder, 
Lazare Weiller recommends two parts of block tin to one 
part of lead. The wire cable and the coupling are both 



Fig. 133. 



i 



IDE 



made of silicon bronze, and thus electrolytic action is 
avoided. 

A very ingenious joint requiring no solder has recently 

Fig. 134. 




-CP' 



been introduced by Messrs. Schmidmer & Co., of Niirn- 
berg. This consists of a sleeve made of very ductile 
copper which 4 is placed over the wire ends to be joined, 

Fig. 135. 




and is then twisted up by special tongs. Fig. 133 
shows the sleeve and wire ends before and Fig. 134 after 
twisting. Even fairly large cables and two heavy cables 



398 



ELECTRIC TRANSMISSION OF ENERGY. 



of different sections can thus be jointed as will be seen 
from Fig. 135. The strength of the joint is very nearly- 
equal to that of the conductor itself. 

A very important matter in connection with overhead 
lines is their protection from lightning. The difficulty 
lies not so much in devising apparatus that will conduct 




the lightning discharge to earth as in preventing the 
power current from following the arc established by the 
lightning flash. The ordinary telegraphic lightning 
guards are therefore mostly useless for power lines and a 
large number of special instruments had to be devised for 
this purpose. The simplest and one of the most reliable 
is the Wirt guards which consists of a number of serrated 
metallic cylinders insulated from each other and set 



LIGHTNING GUARDS. 



399 



parallel to each other in a row with very little clearance. 
There are generally seven of these cylinders and the centre 
cylinder is connected to earthy whilst the two outer cylin- 
ders are connected to the two line wires. One such 
group is used for an alternating current circuit up to 

Fig. 137. 




1,000 volts, and for higher pressures more groups are put 
in series and the connections are suitably altered. The 
principle on which this instrument is based is that the 
ordinary power current has not a sufficient pressure to 
leap over from one cylinder to the other, whilst a lightning 
flash does so easily. The cylinders are made up of an 



400 



ELECTRIC TRANSMISSION OF ENERGY. 



alloy of zinc which is incapable of sustaining an arc. 
The precise reason why this Wirt alloy should quickly 
extinguish any arc is not known ; it seems, however, pro- 
bable that on the first passage of the current zinc is 
burned and the zinc oxide volatilized, thus forming an 
insulating atmosphere which prevents the further flow of 
current. For continuous current lines Professor Elihu 
Thomson has devised the arrangement of lightning 
guards shown in Figs. 136 and 137. G is the generator 
and C the line (in this case an arc circuit), each terminal 
of which is protected. The lightning stroke passes from 

Fig. 138. 




L to E and thus to earth, and if the power current 
attempts to follow, the arc thus established is blown 
upwards by the poles of the electro-magnet M. The arc 
is thus transferred to the upper region of the terminals, 
L E, where the distance is greater and the metal not yet 
heated, with the result that the arc is immediately 
broken. A very ingenious lightning guard introduced by 
the Westinghouse Company and applicable to alternating 
and continuous current lines is shown, in sections in Fig. 
138. It consists of a closed box with a fixed carbon 
electrode, E, projecting through the bottom and two mov- 
able carbon electrodes, X, passing through holes in the sides. 
The movable electrodes are attached to pivoted arms and 



LIGHTNING GUARDS. 401 

connected with the lines, the fixed electrode E is con- 
nected to earth. If a lightning flash leaps from one 
carbon to the other and the power current attempts to 
follow the heat suddenly generated within the box 
expands the air with almost explosive force and the two 
movable electrodes are shot outwards, thus rupturing 
the arc. The motion is arrested by indiarubber buffers 
at the top and the arms immediately fall back into their 
normal position so as to be ready for the next stroke. 



D D 



CHAPTEE XII. 

Examples of Dynamos and Motors — Crompton — Edison -Hopkinson — 
Wolverhampton — Siemens — Brush — Mordey — Kapp — Brown — Wen- 
strom — Thury — Oerlikon — A. E. G. Company of Berlin. 

The previous chapters dealt with the general principles 
of electric power transmission, and with the conditions to 
be fulfilled by the various parts of the plant, without 
entering into the details of any inventor's so-called 
" system " or any maker's special apparatus. The ques- 
tion of system — in so far as the term applies to some 
patented arrangement for which the inventor claims that 
it is the best under all circumstances — is becoming of less 
importance year by year. Experience has shown that in 
power transmission, as in lighting, no inventor's particular 
system is universally applicable, and that the success of 
such works is mainly dependent upon the common sense 
and engineering skill of the men who plan them, and 
the less they are trammelled by adherence to any cut and 
dried system the better. 

An electric power transmission is a very complex piece 
of engineering. To begin with, at one end we have the 
apparatus for producing the power. If this be derived 
from water, it means impounding reservoirs, dams, sluices, 
heavy foundations for the machinery, turbines or water- 
wheels, provision for floods, regulating appliances, and all 
the gear for getting the power to the generators. Then 
we have the generators themselves, with their regulating 



CROMPTON. 403 

appliances, the line, the motors at the other end, more 
regulating appliances, and the gear for delivering the 
power where wanted. The transmission plant as a whole 
requires, therefore, the services of a civil engineer, a 
mechanical engineer, and an electrical engineer. With 
the work of the civil and mechanical engineer this book 
is not concerned. As regards the electrical part of the 
subject, this has been treated in the previous chapters, 
except as regards the more minute details of apparatus. 
A comprehensive treatment of this part of the subject 
would, however, require far more space than can be 
given in this book, for it would be nothing less than a 
treatise on the design and manufacture of dynamos, alter- 
nators, transformers, switchboards, and other accessories 
Of books treating those subjects more or less in detail, 
there are already several in the market, and it is there- 
fore not necessary to describe such machinery here at 
any length. In order, however, to give the student some 
idea of the practical construction of dynamo-electric 
apparatus, a few examples are given in the following 
pages. In some cases the dynamos described were con- 
structed for lighting ; but, after what has been said in 
the earlier parts of this book, it will be clear to the 
reader that any lighting machine can also be used for 
power purposes. The list of machines described is neces- 
sarily incomplete ; in fact, some amongst the best 
machines are not included, the reason being partly want 
of space and partly the maker's reluctance to publish 
details. 

The Crompton Dynamo. — Fig. 139 shows a perspective 
view, and Fig. 140 an elevation of a 100 horse-power 
Crompton motor, largely used for mining work. The 
field consists of two horse-shoe magnets producing four 



404 



ELECTRIC TRANSMISSION OF ENERGY. 



poles, and the armature is a four-pole series-wound drum, 
two sets of brushes only being required. The armature 
core is 24 in. diameter, and consists of a number of thin 
charcoal- iron discs, smooth on the outside, but provided 
on the inside with notches placed equidistantly. Into 
the grooves thus formed radial bars are fitted, by which 

Fig. 139. 




the armature is supported on the central hub, which is 
keyed to the spindle, as shown. The discs are insulated 
from each other, and the armature-bars, which consist of 
stranded and compressed rectangular cable, are held in 
place by a large number of fibre driving-horns, sunk into 
the surface of the armature core. The motor is rated at 
100 B. horse-power at 600 revolutions per minute when 
supplied with current at 455 volts. The magnet cores 



Fiff. 141. 



fe. : , #* 




THE EDISON - HO PKINSON DYNAMO. 

To face page 405. 



EDISON-HOPKINSON. 



405 



are of wr ought-iron, carried on gun-metal brackets. The 
armature contains 358 conductors, and the commutator 
179 bars. The induction in the armature core is 10,000 
and that in field magnet cores is 15,000 C.G.S. lines per 
square centimetre. The efficiency of this machine is 
given by the makers as 93 per cent. 

The Edison- Hopkins on Dynamo. — This machine is the 

Fig. 140. 




b~r r-rr 8 !^: 



result of important improvements made by Dr. Hopkinson 
in the original Edison machine. Fig. 141 illustrates one 
of the latest machines of the improved type as made by 
Messrs. Mather and Piatt for the Central Electric Light 
Station of the Manchester Corporation. The following 
particulars are given by the makers : — Speed 400 revolu- 
tions, output 590 amperes at 410 volts, armature resis- 
tance *017 ohms, field magnet shunt-wound resistance 



406 ELECTRIC TRANSMISSION OF ENERGY. 

52*7 ohms. Two of these machines were tested by work- 
ing one as a generator, and the other as a motor with 
spindles rigidly coupled. The power is thus circulated 
between the two machines, and only the loss of power 
has to be supplied from outside, which in this case was 
done by placing a third machine in series with the two 
machines to be tested. The makers found that the 
efficiency of the two combined machines when tested in 
this manner was 90-5 per cent giving a/ 90*5 = 95 per 
cent, efficiency for each. The total weight of the machine 
is a little over 24 tons, and that of the armature alone is 
close upon 3 tons. 

The Wolverhampton Dynamo. — The machines made by 
the Electric Construction Corporation of Wolverhampton 
are all bi-polar, with either single or double horseshoe 
magnets, the latter for larger sizes. One of these is 
illustrated in Fig. 142. Four machines of this size are in 
use at the power-house of the Liverpool Electric Rail- 
way, the output of each is 475 amperes at 500 volts, the 
speed being 400 revolutions per minute. A good feature 
in the mechanical design is the coupling between the 
armature and the rope pulley, whereby it is rendered 
possible to remove the armature for repairs without 
having to take the driving ropes off. Machines of this 
type have been built up to 2,000 volts. 

Siemens Dynamo. — English and Continental practice 
differ sometimes very much. Thus Messrs. Siemens and 
Halske of Berlin prefer for large dynamos the multipolar 
type, whereas the London firm of Messrs. Siemens 
Brothers are in favour of the two-pole type for all sizes. 
The multipolar type is undoubtedly lighter in large sizes, 
whilst the two-pole type has the advantage of simplicity 
in construction and fewness of parts. The armature is 



to 

• I— I 




TO 







MORDEY. 407 

smaller in diameter, and contains a smaller number of 
active conductors. When wages are high and materials 
cheap the two-pole type may thus be economically 
possible even for large sizes. Messrs. Siemens, of London, 
have introduced a high voltage machine with automatic 
regulation for constant current. The regulation is 
effected by shifting the brushes into positions of higher 
or lower E.M.F. on the commutator. The rocking frame 
which carries the brushes is geared with the dynamo 
shaft by ratchet wheels, crank motor pawl. The latter 
is controlled by a solenoid through which the external 
current passes, and accordingly as the current is above 
or below its normal value, the solenoid throws the pawl 
into gear with either one or other ratchet wheel, thus 
shifting the brushes into a position of lower or higher 
E.M.F. The dynamo illustrated in Fig. 143 is direct- 
driven by a compound steam engine at 300 revolutions 
per minute, and is intended for an output of 10 ampferes 
at a maximum pressure of 1,800 volts. The field is of 
the double magnet Manchester type, and is series wound. 
The armature is of the ring type with a core 30 inches 
diameter by 17 inches long, and the commutator has 200 
parts. 

The Brush Dynamos. — Fig. 144 and 145 illustrate the 
two types of dynamos at present made by the Brush 
Electrical Engineering Company. Both types are now 
much in favour with many English makers and need no 
special description. Fig. 146 shows the Mordey Victoria 
alternator, with exciting dynamo mounted on the same 
spindle. The revolving field magnet system consists of 
two heavy iron castings, with projecting polar extensions 
facing each other, but with sufficient clearance for the 
fixed armature between them. The latter is built up of 



408 



ELECTRIC TRANSMISSION OF ENERGY. 



segmental coils, consisting of flat copper strip wound with 
insulating material over slate cores, and then covered 
with a special enamel to insure high insulation. Each 
coil is held by german silver attachments and bolts in a 
gun-metal frame which is made removable for repairs. 
Owing to the absence of iron within the armature coils 

Fig-. 144. 




the self-induction, and consequently the drop of pressure 
between no load and full load, is remarkably small. 

Kapp Dynamos. — One of the earliest forms of the 
author's dynamos^ as made by Messrs. Allen and Co. and 
used chiefly for ship lighting, is shown in Fig. 147. The 
type is so well known that no special description is 
required. A multipolar type adopted by Messrs. Johnson 
and Phillips, for central station and power purposes, is 
shown in Fig. 148. The machine illustrated is driven by 



Fig. 145. 




Fig. 146. 





fee 

s 



KAPP, 



411 



a triple expansion Davy-Paxman engine at 120 revolu- 
tions per minute, and has an output of 500 amperes at 
260 volts or 130 K.W. The field has 8 poles and the 
armature is drum-wound with series end connections so 
as to necessitate only two sets of brushes 135° apart. A 

Fig. 148. 




machine of the same type, but with a four pole field and 
supplying current for a military electric railway, has the 
following constructive data — output 47 K.W. at 450 volts, 
speed 200 revolutions per minute, armature core 31 inches 
diameter by 20 inches long, wound with 470 bars with 
series end connections. Field magnets of cast steel, 



412 



ELECTRIC TRANSMISSION OF ENERGY. 



diameter of radial magnet cores 15 inches. The field 
magnets are compound wound, the shunt exciting power 
being 18,000 and the series exciting power 5,000 ampere- 
turns. 

The original type of the author's alternator, as made 
by the Oerlikon works and largely used in Continental 

Fig. 149. 




lighting and power stations, is shown in Figs. 149 and 
150. The field system consists of two sets of magnets, 
one on either side of the armature, with rectangular pole 
faces and circular yokes. The armature core is composed 
of charcoal iron strip coiled up with paper insulation over 
a gun-metal supporting wheel, to form a narrow and deep 
ring to w r hich lateral strength is given by steel bolts 
inserted radially as shown. The core thus formed is 



KAPP. 



413 



carefully insulated with mica and press-spahn and the 
armature coils are wound transversely over it, and held 
in place at the outer and inner circumference by driving 
pieces of insulating material. A more modern form of 
the author's alternator is shown in Fig. 151, which repre- 
sents a type recently introduced by Messrs. Johnson and 

Fig. 150. 




Phillips for lighting and power purposes. In this type 
the armature is fixed and the field magnet system revolves. 
The latter consists of two claw-shaped steel castings with 
exciting coil between them, whereby opposite polarity is 
produced on alternate polar faces. The armature con- 
sists of as many segments as there are poles, each segment 
separately supported by gun-metal brackets and steel 



414 ELECTRIC TRANSMISSION OF ENERGY. 

bolts in an external cast-iron shell, and therefore easily 
removable. Each segment consists of a core of charcoal 
iron plates of such shape as to form two longitudinal 
grooves in which is placed the armature coil. The latter 
may, before the core plates are inserted, be insulated all 
over its surface to any desired thickness, thus rendering 
this type of machine specially suitable for long distance 
transmission at high pressure. 

A plant of this kind has recently been made by Messrs. 
Johnson and Phillips for the Sheba Gold Mines in South 
Africa, where power is transmitted by two phase current 
at 3,300 volts over a distance of five miles. At the 
generating station where water power is available there 
are two 132 Kwt. two phase alternators of the type illus- 
trated in Fig. 150, and at the motor station the pressure 
is reduced by step-down transformers to 100 volts, and 
this low pressure current is supplied to the various motors 
driving the stamps and other machinery. 

The Brown Dynamos. — For continuous current trans- 
mission plant Mr. Brown employs the type of machine 
shown in Fig. 152. The field is of the Manchester type, 
with cast-iron pole pieces and circular magnet cores, the 
latter being fitted flat against the pole pieces, and not 
let in as is the usual practice. The bottom pole piece 
is cast in one with the bed-plate and bearings. The 
armature is of the ring type, and very carefully insulated, 
so that the use of these machines becomes possible up to 
3,000 volts, and even more. 

For alternating current work Mr. Brown has adopted 
the type of generator shown in Fig. 153. The field 
magnet system consists of a massive yoke ring with 
magnet cores projecting radially inward. The armature 
is of cylindrical shape, and the core is built up in the 



to 

s 




416 ELECTRIC TRANSMISSION OF ENERGY. 

usual way of iron disks. The armature is wound drum 
fashion, and the ends of the coils on either side are pro- 
tected by special gun-metal rings. In some cases the 
machine is built with a vertical shaft, so that the arma- 
ture may be carried directly on the turbine spindle. 



Fiff. 153. 




Fig. 154 shows a Brown multiphase motor. Both the 
field and the armature conductors are laid in holes very 
close to the circumference so as to reduce magnetic 
leakage. The armature in larger machines is wound 
with three distinct circuits, so as to form a star connection 
with one common centre and three free ends, which are 
brought out to three insulated contact rings, each pro- 



BROWN. 417 



vided with a brush, the three brushes are joined to a 
rheostat with multiple contact switch. At starting the 
whole of the resistance is in circuit, and as the motor 
begins to work the resistance is gradually reduced until 
at full speed the resistance is completely cut out. The 



Fig. 154. 



single phase motors are of the same appearance as Fig. 154, 
and the starting is effected by means of the trans- 
former and condenser arranged as shown in Fig. 119. 
The test recorded in Chapter X. refers to a motor of 
this kind. 

Wenstrom's Dynamo. — The late Mr. Wenstrom has 



418 ELECTRIC TRANSMISSION OF ENERGY. 

been one of the pioneers in multiphase working, and was 
also the first to employ buried conductors in the arma- 
ture. The alternator now made bv his firm in Vesteras, 
Sweden, is of the same type as Brown's, and is made for 
either single or three-phase currents. The armature is 
drum wound with star connection, the conductors being 
heavy bars placed in insulated holes close to the external 
circumference of the core. The following description 
refers to a 100 horse-power three-phase generator, of 
which four are used in the transmission plant of Hellsjon 
Grangesberg, Sweden. The field has 14 poles, and the 
speed is 600 revolutions per minute, giving a frequency 
of 70 cycles per second. The armature contains 84 holes, 
and there are two conductors in each hole, making in all 
168 conductors, or 56 conductors per phase. The current 
in each phase is 190 amperes, and the effective pressure 
150 volts, giving an output of 85*5 apparent Kwt., 
which, with a power factor of 88 per cent., makes the 
true output 100 horse-power. The armature weighs 
15 cwt., and the complete machine 3 tons. One of the 
advantages of machines having iron in the armature is 
their perfect safety in case of a short circuit on the line. 
In the event of a short circuit the self-induction of the 
armature prevents the current rising too much. The 
machine under notice gives when working at full load, 
and under full exciting current on short circuit, only 
double its normal current. Of the four machines in the 
power-house two are working in parallel for power 
purposes, one is used for lighting, and the fourth is kept 
in reserve. Each machine is driven by its own turbine. 
In the lighting machine only two of the phases are used, 
whereby only two-line wires are required. The power 
lxne ? which is 8*5 miles long, consists of three 160 mils. 



WENSTROM. 



419 



bare copper wires, carried on Johnson and Phillips' oil 
insulators on wooden posts 28 feet high, underground 
cable being used for crossing railways and high roads. 
The pressure is raised at the power-house by step-up 
transformers to 5,200 volts in each branch, making the 
difference of potential between any two-line wires 9,000 
volts. The power is taken off at various points on the 
line by means of step-down transformers and three-phase 

Fig. 155. 




motors, of which there are five ot 45 horse-power, three 
of 30 horse-power, and one of 9 horse-power. The type 
of motor employed is illustrated in Fig. 155. The small 
motor is provided with a squirrel cage armature, as 
shown in Fig. 156, but the larger motors have armatures 
wound with three closed circuits and provided with con- 
tact rings, as shown in Fig. 157. 

Thury Dynamo. — The makers of this machine (L'ln- 
dustrie Electrique, of Geneva) have developed a very 



420 



ELECTRIC TRANSMISSION OF ENERGY. 



interesting system of power transmission and distribution 
by means of constant current and variable Voltage, accord- 
ing to the requirements of the customers receiving power 
from the line. The generators employed in these plants 

Fig. 156. 




are of the type shown in Fig. 158. They are six-pole 
continuous-current dynamos, with drum-wound arma- 
tures. Great precautions are taken as regards insula- 
tion, not only of the winding from the core, but of the 

Fig. 157. 




machine itself. Thus the armature core is insulated from 
the shaft, and to prevent sparking from the armature 
conductors to the pole-pieces, the whole armature, after 
winding, is wrapped round with layers of paper and 
shellaced cloth. The field-magnets are insulated from 
the bed-plate by thick layers of mica, and the bed-plate 



422 ELECTRIC TRANSMISSION OF ENERGY. 

itself is insulated from the ground by porcelain insu- 
lators, with circular channels filled with resin oil. The 
machine illustrated has an output of 47 amperes at 
1,100 volts when driven at a speed of 475 revolutions. 
Eighteen of these machines are employed in the power 
transmission between the river Gorzente and the town of 
Genoa. The total available fall of water is 1,200 feet, 
and this is taken up in three power stations, which divide 
the head of water between them. The two larger stations 
are each fitted with eight generators, which are coupled 
in series, and the current is sent to Genoa by an over- 
head line supported on oil insulators, the w T ire being 350 
mils, diameter. Special automatic apparatus is employed 
to keep the current constant at 47 amperes, whatever 
may be the variation in pressure produced by the stopping 
or starting of the motors on the circuit. The motors are 
all series-wound Thury machines, and are of the two-pole 
type up to 15 horse-power, four-pole type between 15 and 
30 horse-power, and six-pole type for larger powers. 
These motors are placed on the premises of the power 
company's customers, and are all connected in series on 
the line, which is about twenty-seven miles long. The 
speed of the motors is regulated by a centrifugal governor 
acting upon the field-winding in such a way that the ex- 
citing power is decreased as the speed increases, and vice 
versa. To stop a motor the customer has simply to short 
circuit it. The total power thus distributed in Genoa is 
about 1,000 horse-power. 

Oerlihon Dynamos. — The continuous-current machines 
for moderate powers, built by the Oerlikon Works, are of 
the " Manchester " type, Fig, 28, and for larger sizes of 
the multipolar type, the latter with vertical spindles for 
direct coupling to the turbine shaft where such an arrange- 



OERLIKON. 



423 



ment is expedient. In some cases alternators are also 
arranged in this manner, and to relieve the thrust bearing 
or foot step of the turbine from the weight of the re- 
volving masses, these makers have introduced a most in- 
genious magnetic balancing arrangement, consisting of 
an annular electro-magnet and ring-shaped armature of 

Fig. 159. 




coiled iron strip. The latter is firmly attached to the 
turbine shaft, and revolves in close proximity under the 
poles of the fixed magnet. The magnet is excited by a 
continuous current, and by suitably proportioning the 
surface and number of poles any desired magnetic pull 
upwards can be obtained, thus relieving the bearings of 
down thrust. The action of this device is more certain 



424 



ELECTRIC TRANSMISSION OF ENERGY. 



and the loss of power smaller than with any form of 
hydraulic balancing gear yet introduced. 

In addition to the author's types of alternators, which 
have already been illustrated, the Oerlikon Works make 
a three-phase generator of the type shown in Figs. 159, 
160, and 161. The field-magnet system is of the single 

Fig. 160. 




coil claw type, and the armature consists of a continuous 
ring of iron plates with teeth projecting inwards. The 
teeth are widened out at their inner ends, but not suffi- 
ciently to meet. The object of leaving spaces between the 
ends of the teeth is to permit of the armature coils being 
inserted and afterwards squeezed tight against the narrow 
part of the tooth by a special clamping too]. The num- 



OERLIKON. 



425 



ber of poles is to the number of coils as 2 : 3, and the 
coils are coupled up to form the three circuits of the 
three-phase system. As the gaps in the inner surface of 
the armature produce fluctuations in the magnetic flux 
which would cause waste of power and heat the face of 
the pole-pieces if these were made solid, subdivision of 

Fig. 161. 




the metal is obtained by tipping the pole-pieces with thin 
sheet-iron stampings, as shown in Fig. 160. 

Figs. 162 and 163 show details of the construction ot 
the Oerlikon transformer. The coils are wound on 
separate paper sleeves and are placed over the central 
core, which is built up of plates of different widths so as 
to approach a circular shape. The magnetic circuit is 



fee 



be 




OERLIKON. 



427 



closed by a top and bottom yoke clamped tightly in the 
two halves of the cast-iron case. For three-phase trans- 
formers a vertical design is adopted, consisting of three 
cores joined at both ends by annular yokes. The surface 
of small and moderate-sized transformers is sufficient to 
radiate all the heat generated into the air, but as with 

Fig. 164. 




increase of size the surface augments only as the square 
of the linear dimensions, whereas the bulk and power 
wasted grow as the cube of the linear dimensions, a point 
is finally reached where even the most efficient type of 
transformer cannot be kept cool enough by air circula- 
tion, and it becomes necessary to fill the transformer case 
with rosin oil, and in some cases to circulate the oil by 
means of a pump through cooling tanks. 



428 



ELECTRIC TRANSMISSION OF ENERGY. 



The general design of single and multiphase motors 
made by the Oerlikon Works is shown in Figs. 164 and 
165. Small motors have an armature with squirrel cage 
winding, and in larger motors the armature is drum wound 
with three distinct circuits and the winding is connected 
to contact rings as already explained. 



Fig. 165. 




The Oerlikon Works are driven by electric power 
brought from Bulach, over a distance of fourteen and a half 
miles. In the generating station there are three 200 horse- 
power turbines, and to the vertical shaft of each is coupled 
direct a three-phaser giving at 180 revolutions in each 
phase 1,500 amperes at 50 volts. The frequency is 48. 
Each generator is connected with the low pressure winding 
of a transformer, and the high pressure winding is 



OERLIKON. 429 

arranged to raise the pressure in each phase to 7,500 volts 
or 13,000 volts between any two line wires. The coupling 
of the phases in the generators and in both windings of 
the transformer is star fashion, the common centres being 
in metallic connection and also well earthed. Ordinarily 
only two generators are in use and the corresponding 
transformers are coupled parallel on the high pressure 
side to the three line wires, which consist of 160 mil bare 
hard drawn copper wire carried on oil insulators. The 
posts are of wood 33 feet high, and are placed at an 
average distance of 330 feet. In addition to the three 
power wires they carry two telephone wires, lead and 
return. At the motor station in the Oerlikon Works the 
current is transformed down in two transformers, with 
primaries in parallel and secondaries in series, and is then 
led into a three-phase motor which drives the whole of 
the works. A phase rectifier is used on the secondary 
circuit at the motor station. At starting one turbine only 
is at first used, and the armature circuits of the motor are 
closed by a three pole switch. When the motor is under 
way the second turbine is started and the corresponding 
transformer thrown into parallel with the first. No syn- 
chronizer or other appliance is used^ the machines pulling 
each other into place without any difficulty when the 
speeds are approximately equal. 

A similar transmission plant, but combined with dis- 
tribution of current between a number of small consumers 
of light and power, is that between Killwangen and 
Zurich, a distance of twelve and a half miles. The gene- 
rator is a 300 horse-power three-phaser driven by a 
turbine, and a step-up transformer raises the pressure in 
each phase from 50 to 3,000 volts for transmission to 
Zurich on an overhead line. From a central point in 



430 ELECTRIC TRANSMISSION OF ENERGY. 

Zurich branch lines are taken to the different customers 
for the supply of light and motive power by means of 
step-down transformers. The motors used are 3 horse- 
power^ 10 horse-power, and 20 horse-power. Variations 
of pressure in the power circuits do, of course, not affect 
the speed of the motors as this depends only on the 
frequency, but such variations would affect the lighting 
service, and to overcome this difficulty a fourth line wire 
is used connecting the centres of the star coupling at 
either end. Similar three-phase plants for light and 
power combined are at work or in course of erection at 
Wangen (Wiirtemberg) for 350 horse-power, Percine 
(Tyrol) for 100 horse-power, St. Etienne (France) for 
1,000 horse-power, and Florensac (France) for 100 horse- 
power. 

The A. E. G. Dynamos. — Some account of continuous 
current plant for power transmission, made by the Allge- 
meine Elektrizitats Gesellschaft of Berlin, has already 
been given in a previous chapter. In addition to con- 
tinuous current work this firm make a speciality of three- 
phase power transmission, in which branch their elec- 
trician, Herr Dolivo von Dobrowolsky, has been one of 
the earliest pioneers. The results of tests with one of 
his motors has already been given in Chapter X, and 
Fig. 166 shows a novel application of his motors for 
industrial purposes. The centrifugal machines in sugar 
refineries have hitherto been worked by belt, but con- 
siderable difficulties were experienced with the bearings 
on account of the side stresses produced by the belt, whilst 
much time was lost in bringing the machine up to speed 
after each charge. These drawbacks have now been 
overcome by the use of a three-phase motor coupled direct 
on the spindle of the centrifugal machine. Not only are 



Fig. 166. 




CENTRIFUGAL MACHINE WITH DOBROWOLSKY MOTOR. 

To face page 430. 



DOBROWOLSKY. 431 

all side stresses thereby completely avoided, reducing 
wear and tear and economizing power, but the machines 
may be brought up to full speed much more quickly, 
and the output of the works is thus very considerably 
increased. 



THE END. 



LIST OF NUMBEEED FOEMUL.E WITH THE 
PAGES ON WHICH THEY APPEAR. 



1. Max. E.M.F. of Ideal Alternator . 

2. Mean E.M.F. of Ideal Alternator 

3. E.M.F. in Hefner- Alteneck Armature 

4. 5, 6. Average E.M.F. in Gramme Armature 
7, 8. Torque of Motor Armature 
9, 10, 11. Energy from Motor Shaft . 

12, 13, 14. Energy in Horse-power 

15. Current in Armature of Compound Dynamo 

16. E.M.F. at Brushes of Compound Dynamo 

17. E.M.F. at Terminals of Compound Dynamo 

18. Efficiency of Compound Dynamo . 

19. Current in Armature of Compound Motor 

20. E.M.F. at Brushes of Compound Motor 

21. E.M.F. at Armature of Compound Motor 

22. Efficiency of Compound Motor 

23. 24, 24 a, 24 b. Strength of Field . 
25, 25 a, 26, 26 a. Exciting power required 

27. Magnetic Resistance of Leakage Field 

28. Loss of Flux by Leakage 

29. Maximum Commercial Efficiency 

30. Loss of Current by Leakage . 

31. Electrical Efficiency 

32. Commercial Efficiency . 

33. 34. Current received by Motor 
35, 36, 37. Counter E.M.F. of Motor 
38, 39, 40. Effective E.M.F. of Alternator. 

41. Maximum E.M.F. of Self-induction . 

42. Effective Maximum E.M.F. of Self-induction 

43. Effective Power of Alternator 

44. Current of Alternator . 

45. 46. Power absorbed by Alternate Current Circuit 

FF 



115, 1 



TAGE 

. 68 
. 70 
. 83 
91, 94 
. 100 

103, 104 

106, 107 
. 110 
. 110 
. 110 
. 110 
. 11 
. 11 
. 11 
. 11 
19, 120, 12] 
. 122 
. 130 
. 130 
. 155 
. 187 
. 190 
. 193 
. 195 

195, 196 
214, 216, 217 
. 220 
. 220 
. 224 
. 225 

227, 228 



434 LIST OF NUMBERED FORMULAE. 

PAGE 

47, 48. Power given by Dynamo 228 

49, 50. Power absorbed by Alternate Current Circuit . 229, 230 

51. Value of DK 2 235 

52, 53. Power by Wattmeter 236 

54. Phase Difference . . .238 

55. Angle of Lag . . .238 

56. Power in Watts .240 

57. Approximate exciting power in Ampere-turns . . . 250 

58. Condenser current — capacity of Line 280 

59. 60, 61. Capacity of Concentric Cable 280 

62. Magnetic Slip . . 305 

63. Tangential Pull of Motor 319 

64. Ampere-turns 320 

65. Lines of Force 320 

66. Power of two-pole Armature 321 

67. Effective current 321 

68. 69. Effective E.M.F 322, 325 

70, 71, 72. Effective current in Amperes .... 328, 333 

73. Tangential pull of Armature in Kilogrammes . . . 334 

74. Torque in Kilogramme-centimetres ..... 334 

75. Current in Amperes 334 

76. Torque allowing for Leakage 334 

77. Power in Watts allowing for Leakage . . .. . . 335 

78. Current for three-phase Motor ...... 339 

79. Effective E.M.F. in three-phase Motor 340 



INDEX. 



Absolute system of electro-mag- 
netic measurements, 34, 59. 

and practical units, 105. 

Advantages of electric transmis- 
sion, 9, 16. 

A. E. G. dynamos, 430. 

Allen and Co.'s Kapp dynamo, 
408. 

Alternating current dynamo, 66. 
equations, 68, 69. 



dynamometer, 231. 



— currents, 11. 

for arc lamps, 254. 

importance of for long- 
distance transmission, 208, 389. 
- and Lenz's law, 222. 
and power transmis- 



sion, 255. 

and transformers, 210. 

Alternators, Brown's, 414, 416. 
co-efficient for E.M.F. of, 



215. 



compared with continuous 



current machines, 384, 389. 
cost of line for, 389. 



electromotive force of, 211, 

256. 

Kapp's, 412. 

low voltage generator may 

drive high voltage motor, 258. 

- margin of power, 274. 
measuring the power of, 217, 



224. 



— Mordey-Victoria, 407. 

— reaction of armature, 271, 
273, 278. 

- self-induction in, 243, 278. 
small, objections to, as 



Alternators, stress on motor, 266. 
Ampere, unit of current, 60. 



motors, 287. 



meters, three, test for power 

of alternators, 225. 
Ampere's rule for direction of 

magnetic effects of current, 39. 
Ampere-Turns, 115, 311. 

and induction, 317, 

326. 

Andrew's field magnet, 36. 
Angle of lag, 223. 
Arago's rotation, 289, 293. 
Arc lamps, alternating currents 

for, 254. 
Armature bars, effect of resistance 

of, 316. 

brushes, position of, 88. 

cores, sub-division of, 94. 

reaction, 138, 140, 248, 262, 

271, 278, 300. 

, connections of, for multi- 
polar machines, 132. 

covering of wires for, 191. 

currents in rotary field, 307. 

definition of machine by di- 
mensions of, 129. 

effect of, on magnetic field, 



94. 



56. 

electromotive force in, 93, 

Gramme, 85. 
- Hefner- Alteneck, 81. 
— loss Sof energy by heating, 
192, 316, 322. 

; ' magnetic slip" of, 302, 305, 



322. 



Pacinotti, 85, 89, 140. 
prevention of heating of, 



160, 316. 



436 



INDEX. 



Armatures, self-induction in, of 

alternator, 243, 278. 
Siemens' or shuttle -wound, 

73. 

winding of gramme, 89. 

Arno's tests of single-phase motor, 

366. 
Ayrton and Perry on government 

of motors, 170, 180. 
Ayrton's test for self-induction in 

alternator, 244. 

Back electromotive force, 323, 

337, 347. 
Baily, Walter, rotary field motor 

invented by, 289. 
Barlow's wheel, 61. 
Bessbrook and Newry Kailway, 

15. 
Binding-in line wires, 394. 
Blakesley's split dynamometer 

test for lag, 238. 
Borel and Paccaud motor, 291. 
Brown dynamos, 414, 416. 
maximum variation of speed, 

202. 



— single -phase motor, Arno's 
tests of, 366. 

starting device of single - 



phase motors, 368, 417. 
Brushes, armature, position of, 

88. 

for multipolar machines, 132. 

Brush dynamo, 407. 

field magnets, 108, Figs. 46 

and 47. 

Burgin machine, dynamo and 
motor characteristics, 141, 201. 

Cable, Ferranti concentric, capa- 
city of, 279. 
Capacity, 59, 60, 278, 286. 

in relation to " frequency," 

255. 

Cells, secondary, use of, 3. 
C. G. S. system, 34, 59. 
Characteristic curves, 135, 142, 

145, 199, 207. 
Chretien's estimate of water 

power in France, 12. 
City and South London Railway, 

20. 



" Clock Diagram," 213, 221, 245, 
256, 268, 274, 281, 284, 309, 328, 
356. 

Coal, horse-power from, 12. 

Co-efficient for E.M.F. of alter- 
nators, 215. 

of self-induction, 219, 248. 

Commercial efficiency of motor, 

54, 153, 155, 157, 192. 
Commutator, 71. 

sub-division of, 107. 

Compound winding for regulation 

of speed, 151, 156. 

wound dynamo, 161. 

as a motor, con- 
nections for, 177. 

motor, speed for maxi- 



mum commercial efficiencv, 
157. '■ 

Concentric cable, Ferranti, capa- 
city of, 279. 

Conductors, properties of line, 
390. 

Lord Kelvin's Law of Eco- 
nomy of, 372. 

weight of, for economical 

transmission, 380. 

Conservation of energy, 22. 
Constant current, distribution of 
energy at, 179. 

pressure, distribution of 

energy at, 170. 

speed, compound winding 

for, 151, 156. 

Continuous current dynamo, 71. 

motor, force of, com- 
pared with rotary field motor, 
319. 

compared with al- 



ternators, 384, 389. 
Conversion, efficiency of, 110. 
Copper, comparison with other 

conductors, 390. 
temperature co - efficient, 

392. 



weight of, for economical 

transmission, 380, 389. 
Cost of line for transmission of 

energy, 370. 
Coulomb, unit of quantity, 60. 
Counter electromotive force, 49, 

50, 75, 189, 323, 337, 347. 



INDEX. 



437 



Counter electromotive force, equa- 
tions referring to, 50, 51, 52, 55, 
56, 83, 175. 

of motor, relation 

to E.M.F. of source of supply, 
54, 154. 

Coupling, " Link," 343. 

''Star," 342. _ 

Weiller's joint, for line 

wires, 396. 

Crompton dynamo, 403. 

Held magnet, Fig. 30. 

Current, distribution of energy at 

constant, 179. 
— - and efficiency, f ormulse for, 
195. 



180. 



external effects of, 37. 

Ampere's rule, 39. 

speed independent of, 103, 
). 

- unit of, 40, 41, 60. 

frequency, 218, 251. 

Currents, alternating, 11. 

eddy, 141. 

multiphase, 11. 

Curves, characteristic, 135, 145, 
199, 207. 

E.M.F. , should be sinusoi- 
dal, 384. 

horse-power, 143. 

- magnetization, 125. 



Cylinder type of armature, 112. 

Danger from high E.M.F., 169. 

Dead points of Siemen's arma- 
ture, 75, 76. 

Debrowolsky, von, combined star 
and link winding, 344. 

phase-rectifier, 385. 

and self -regulating machines, 

202. 

three - phase transmission, 

430. 

Definition, unit current, 40, 41. 
, electro - motive force, 

43. 

, magnetic pole, 33, 37. 

De Meriten's field magnet, Fig. 

49. 
Deprez, Marcel, test of gramme 

dynamo by, 114, 139. 

on torque, 101. 



Design of machines, characteris- 
tics for, 126. 

Diagram, clock, 213, 221, 245, 
256, 268, 274, 281, 284, 309, 328, 
356. 

Difference of potential, 46. 

Disk, Arago's, 293. 

Disk type of armature, 112. 

Distribution of energy at con- 
stant current, 179. 

pressure, 170. 

Drum type of armature, 112. 

Dub's investigations of magne- 
tism, 116. 

Dynamic characteristic, 136. 

Dynamo, A. E. G., 430. 

alternating current, QQ. 

Brown, 414. 

Brush, 407. 

compound, wound, 151, 156, 

157, 161. 

reversal of polarity 

of, 163. 

continuous current, 71. 

Crompton, 403. 

Edison, 203. 

Edison-Hopkinson, 405. 

field of, 8Q, 87. 

Forbes' non -polar, 63. 

Kapp, 408. 

Oerlikon, 422. 

Siemens Brothers, 406. 

Thury, 419. 

uni-polar, 65. 

Wenstrom, 417. 

Wolverhampton, 406. 

Dynamometer, alternating cur- 
rent, 231. 

test for lag, 238. 

Dynamos, formulae for, 111, 228. 

theoretical conditions com- 
pared with motors, 97, 174. 

Dyne, 34, 105. 

Economy of conductors, Lord 

Kelvin's law, 372. 

of electrical power in use, 19. 

Eddy currents, 141. 
Edison dynamo, 203. 
Edison-Hopkinson dynamo, 405. 
field magnet, 113, Fig. 

27. 



438 



INDEX. 



Effective pressure, 215. 
Efficiency, commercial, of motor, 
54, 153. 

of conversion, 110. 

effect of resistance on, 278. 

electrical, 110, 192. 

equations relative to, 51, 55, 

56, 110, 111, 155, 190, 193. 

maximum, commercial, 54, 



155, 157, 192, 195. 

and maximum work, 



148, 152. 

of transmission, 261, 

353. 

— of simple motor, 51, 54. 
- and "Slip," 330. 
and torque, relation of, 



322. 

Electric Construction Corporation 
dynamo, 406. 

current, external effects of, 

37. 

— Ampere's rule, 39. 

Electrical efficiency, 110, 192. 

resistance, 44. 

Electro-dynamic paradox, Gerard - 

Lescuyer's, 166. 
Electro-magnetic measurements, 

absolute system of, 34. 
Electro -motive force, 42, 43, 60. 
of alternating genera- 
tors and motors, 259, 278. 

back, 323, 337, 347. 

■-— counter, 49, 75, 189, 323. 
value of, 50, 54, 



154. 

danger from high, 169. 

equations relating to, 

68, 70, 83, 91, 93, 144, 175, 
211, 219, 220, 322, 325, 340. 
— and horse -power, 144. 
of multipolar machines, 



132. 



256, 273. 



256. 



alternators, 211, 215, 

practical limit, 265. 
of self-induction, 218, 



Elwell-Parker field-magnet, Figs. 

31, 32. 
Energy, conservation of, 22. 
— — developed in armature, 95. 



Energy, general principles of 
transmission of, 1. 

loss of, 57, 192, 370. 

Equivalent magnetic shell, 40. 
Erg, 34, 105. 

Esson's tests for armature re- 
action, 140. 

Ewing, Professor, on hysteresis, 
109. 

Exciting power of machine, 115, 
122, 250, 326. 

formula for, 121, 122, 124, 

250, 339. 

Experiments on self-induction, 

77. 
External characteristics, 144. 

Factor of safety, 392. 
Factories, electric power in, 17. 
Farad, unit of capacity, 60. 
Faraday's lines of force, 24. 

rotating disc, 62. 

Ferranti concentric cable, capa- 
city of, 279. 

Ferraris on theory of single-phase 

motors, 360. 
Ferraris' two-phase motors, 290. 
Field, ampere-turns for, 311, 

326. 

effect on, of " lagging " and 

" leading" currents, 250. 

effect of a revolving, 295. 

"impressed," 309, 326, 337. 

and field current, 337. 

magnetic, 31, 33, 34. 

of dynamo, 86, 87. 

equations for strength 



of, 119, 120, 121, 176, 328. 

must be weak for heavy 

work, 176. 

"primary," 309. 



resultant, and back E.M.F., 

337. 
Field coils, regulation of sj3eed by 

number of, 303. 

current and impressed field, 



337. 



excitation, 326. 
magnets, multipolar, 131. 
types of, 113, Figs. 27 



to 51. 
Fleming on Impedance, 225. 



INDEX. 



439 



Fleming's three-ampere meter test 
for power of alternators, 229. 

Flux, loss of, by leakage, 130. 

Forbes' non-polar dynamo, 63. 

France, water power in, 12. 

Frequency, capacity in relation 
to, 255. 

current, 218, 251. 

Generators, A. E. G., 430. 

alternating, E.M.F. of, and 

motors, 273, 278. 
relation of, to motors, 



259. 

— Brown, 414. 

— Brush, 407. 

— Crompton, 403. 

— Edison-Hopkinson, 405. 

— Kapp, 408. 

— Oerlikon, 422. 

— self-induction and reaction 
in, 278. 

— Siemens Bros., 406. 

— Thury, 419. 

- Wenstrom, 417. 
Wolverhampton, 406. 



Genoa, power distribution in, 
422. 

Gerard-Lescuyer's electro-dyna- 
mic paradox, 166. 

Glow lamps as resistance, 230. 

Goolden and Trotter field mag- 
net, Fig. 35. 

Government of motors, Ayrton 
and Perry on, 170, 180. 

Governors, periodic, 171. 

spasmodic, 171. 

Gramme armature, 85. 

winding of, 89. 

- field magnet, 113, Fig. 48. 
motor, experiments for 



torque, 103. 

ring as two-phase motor, 



296. 
Griscom motors, self-induction 

experiments, 77. 
Guards, lightning, 398. 
Gulcher field magnet, Figs. 44 

and 45. 

Heating of armature, prevention 
of, 160, 316. 



Heating of armature, waste of 

energy by, 192, 213, 322. 

transformers, 427. 

Hefner- Alteneck armature, 81. 

motor, torque of, 103. 

Helios Co.'s motor, 290. 

Henry, unit of self-induction, 

220. 
High tension motor, experiments 

for torque, 103. 
Hopkinson's " characteristics " of 

Siemens dynamo, 142. 
Hopkinson-Edison, dynamo, 405. 
field-magnet, 113, Fig. 

27. 
Horse-power curves, 143. 

developed in armature, 95. 

English, 106. 

standard in metric system, 



106. 



from water, 12. 



Hughes on theory of magnetisa- 
tion, 28. 
Hysteresis, 141. 
Professor Ewing on, 109. 



Impedance, 225. 

" Impressed field," 309, 326, 337. 

Inductance, 221, 284. 

Induction, 123. 

and ampere-turns, 317. 

torque, 317. 

Inductionless resistance for test- 
ing, 230. 

Induction motors, 288. 

self-, in alternators, 243. 

co-efficient of, 219, 248. 

E.M.F. of, 218, 256. 

experimental determina- 
tion of, 349. 

in single-phase motor, 



356, 364. 



unit of, 220. 



Insulators, Johnson and Phillips, 

393. 
Internal characteristics, 144. 
Iron compared with air as path 

for lines of force, 73. 

Magnetic qualities of, terts 

for, 124. 

soft, 30. 



440 



INDEX. 



Jacobi's investigations in magne- 
tism, 116. 

Japing, estimate of power of 
Niagara, 12. 

Johnson and Phillips' insulator, 
393. 

Kapp dynamo, 408, 

413. 

Joints in line wires, 395. 

Jones field magnet, Fig. 37. 

Kapp's device for self -regulating 
constant current motor, 182. 

dynamo, 408. 

field magnets, Figs. 38, 39, 

and 40. 

Oerlikon alternator, 412. 



Kelvin's law of economy of con- 
ductors, 372. 

Kolben's experiments on leakage 
factor, 351, 365. 

Lag, angle of, 223. 

measurement of, 238. 

reduction or avoidance of, 

384. 

Lagging and leading currents, 
effects of, 250, 384. 

Law, Lenz's, and alternate cur- 
rents, 222. 

of magnetic attraction and 

repulsion, 33. 

Ohm's, 43. 



Leading and lagging currents, 

effects of, 250, 261. 
Leakage over commutator, 209. 

factor, 351, 364. 

fields, calculation for com- 
parison of, 129. 

formulae relating to, 



130, 187, 334, 335. 
— loss of current by, 185, 333. 
magnetic, 123, 127, 333, 335, 



364. 
Lenz's law and alternate currents, 

222. 
Life, danger to, from high E. M. F. , 

169. 
Lightning guards, 398. 
Lines of force, effect of iron on 

direction, 85. 
Faraday's, 24. 



Lines of force, unit, 31, 34. 
, binding in wires, 394. 

construction of, 391. 

joints in, 395. 

material for conductor, 390. 

underground, essential in 

populous districts, 389. 

Line, capacity of, 278. 

relation between first cost 

of, and waste of energy, 370. 

weight of, for economical 



transmission, 380. 

with different systems 

of transmission, 389. 

effect of lag upon, 384. 

' 'Link coupling," 343. 

Load of motor, 161. 

margin of, for alter- 
nators, 263, 274. 

Lodge (Oliver) on effect of leakage 
on efficiency, 188. 

London, City and South, Railway, 
20. 

Long distance transmission, im- 
portance of alternating currents, 
208. 

Loss of current by leakage, 185. 

of energy, 57, 107. 

from hysteresis, 109. 

of flux by leakage, 130. 

Magnetic attraction and repulsion, 

law of, 33. 

field, 31, 33, 34. 

, equations for strength 

of, 119, 120, 121, 176, 328. 

— friction, 107. 

intensity of field altered by 



armature, 56. 

— leakage, 123, 127, 333, 335. 

— moment, 40. 

— permeability, 120. 
- pole, unit, 33, 37. 

qualities of iron, tests for, 



124. 



— resistance, 115. 
of leakage field, 130. 

— shell, equivalent, 40. 

— "Slip" of armature, 302, 
305, 322, 353. 

— whirl, 37. 



Magnetisation, curves, 124, 125. 



INDEX. 



441 



Magnetisation, theory of, 28. 
Magnetism, investigations in, 

116. 
Magnets, field, multipolar, 131. 
types of, 113, Figs. 27 

to 51. 
" Manchester " dynamo, 113, 

Fig. 28. 
Margin of power for alternators, 

263, 274. 
Mather and Piatt's dynamos, 

405. 
Maximum efficiency of power 

transmission, 261. 
commercial efficiency, 54, 

155, 157. 

work, law of, 51. 

and maximum effi- 
ciency, 148, 152. 
Measurements, absolute system 

of, 34, 59. 
and practical units, 

105. 
Measurement of power of alter- 
nators, 217, 224. 
Microfarad, sub-unit of capacity, 

60. 
Mining work, dynamo for, 403. 
Moment, magnetic, 40. 
Mordey- Victoria alternator, 407. 

field magnet, 114. 

self-induction tests of, 

244. 
Motor characteristic, 137, 140. 
of Siemens' machine, 



144. 



A. E. G.,430. 
Brown, 414. 



multiphase, 416. 

Brush, 407. 

Crompton, 403. 

Edison- Hopkinson, 405. 

Kapp, 408. 

Oerlikon, 422. 

Siemens Brothers', 406. 

■ Thury, 419. 

Wenstrom, 417. 

Wolverhampton, 406. 

Motors, alternating, current at 

short circuit, 265. 
E.M.F. of, and gene- 
rator, 273, 278, 



Motors, alternating, objections 
to small, 287. 

reaction of armature, 

271, 278. 

relation of voltage to 

generators, 259. 

- self-induction, 278. 
stress at short circuit, 



266. 



— Ayrton and Perry on govern- 
ment of , 170. 
- Borel and Paccaud, 291. 
compound wound, connec- 



tions of, 177. 

— determining conditions for 

speed of, 53. 

effect of lagging and leading 



currents on, 250. 
— efficiency of, 51, 54, 110, 353. 
- Ferraris two -phase, 290. 
formulae for, 111, 175, 195, 



340. 



— Griscom, self-induction ex- 
periments, 77. 

— Helios Co.'s, 290. 

— induction, 288. 

— maximum commercial effi- 
ciency of, speed for, 155, 157, 
195. 

— poliphase, 288, 293. 

— "power factor " of, 349, 353. 

— regulation of speed of, 150. 

— relations between similar, of 
different sizes, 100. 

- rotary field, 288. 

constant voltage, 328, 



331. 

and continuous current 

compared, 319. 

• power and induction, 



321, 



starting conditions, 336. 



theory of, 311. 



self - regulating, 173, 178, 



182. 



series wound, 75, 145. 
shunt-wound, 75. 



158. 



range of self -regulation, 

regulation of speed by 
compound winding of dvnamo, 
161, 163, 



442 



INDEX. 



Motors, shunt-wound, not self- 
starting, 160. 

speed for maximum 

commercial efficiency, 157. 

single-phase, 355. 

Starting devices for, 



367. 



— small, not always suitable 
for dynamos, 134. 

speed of, having regard to 



leakage, 188. 

— starting device for, 205. 

— theoretical reversibility as 
generators, 96, 174. 

- theory of, 97. 
two-phase and three-phase, 



compared, 301, 339. 

Muller's investigations in mag- 
netism, 116. 

Multiphase currents, 11. 

motor, Brown's, 416. 

• Oerlikon, 428. 

Multipolar machines, brushes for, 
132. 

■ current and voltage 

from, 132. 

— field magnets for, 131. 



Newry, Bessbrook and, electric 

railway, 15. 
Niagara, Falls of, power of, 12. 

"frequency" of machines, 

251. 

Non-polar dynamo, Forbes', 63. 

Oerlikon alternator, Kapp's, 412. 

dynamo, 422. 

three-phase generator, 424. 

transformer, 425. 

works, 14. 

Oersted experiment, 294. 

Ohm, standard resistance, 44, 60. 
Ohm's law, 43. 

Over-compounded generator with 
shunt motor, 161. 

Paccaud's motor, Borel and, 291. 
Pacinotti armature, 85, 89, 108. 

reaction in, 140. 

Parallel system of distribution, 
169. 



Parker, Elwell-, field magnet, 
Figs. 31, 32. 

Periodic governors, Ayrton and 
Perry's, 171. 

Permeability, magnetic, 120. 

Perry (and Ayrton) on govern- 
ment of motors, 170, 180. 

Phase-rectifier, 385. 

Phoenix machine, reaction in ar- 
mature of, 140. 

Phosphor-bronze wire, 390. 

Polarity of compound machine, 
reversal of, 163. 

Poliphase motors, 288, 293. 

Portrush electric railway, 15. 

Potential, 44. 

difference of, 46. 

Power, of alternators, measure- 
ment of, 217, 225. 

comparison of, derived from 

water and coal, 12. 

" Power factor " of motors, 349. 
Power as a function of speed, 345. 

and induction, relation of, 

in rotary field motors, 321. 

margin of, for alternators, 



263, 274. 
— measurement of, by Watt- 
meter, 233. 

in rotary-field motors, equa- 



tions of, 321, 325, 335. 

— transmission by alternating 

currents, 255. 

of, maximum efficiency, 

Tesla's system, 291. 



261. 



unit of, watt, 60. 

Pressure, effective or virtual, 215. 
Pressure, distribution of energy 

at constant, 170. 
Primary field, 309. 
Protection from high E.M.F., 169. 

Quantity, unit of, coulomb, 60. 
Quadrant, unit of self-induction, 
220. 

Railways, electric, 15, 20. 
Range of counter E.M.F. and 

effect on efficiency, 198. 
of self -regulation of motors, 

158. 



INDEX. 



443 



Reaction, armature, 138, 140, 248, 
262, 271, 278, 300. 

Regulation of speed by charac- 
teristics of machines, 199. 

by compound winding, 



151. 



of motor by compound 



winding of dynamo, 161, 163. 
by resistance, 150. 



Resistance of armature bars, 
effect of, 316. 

effect of, on efficiency, 278. 

electrical, 44, 60. 

inductionless, for testing, 

230. 

of line conductors, 390. 

magnetic, 115, 130. 

- regulation of speed by, 150. 
in starting motor, 336. 



Reversal of polarity of compound 
machine, 163. 

Revolving field, effect of a, 295. 

Rheostat, liquid, for starting 
motor, 205. 

Rhine, falls at Schaffhausen, 
power of, 12, 14. 

Rotary field motors, 288. 

advantages over con- 
tinuous current motors, 319. 
theory of, 311. 



Rotating disc, Faraday's, 62. 
Rotation, Arago's, 289. 

Safety, factor of, for line wire, 

392. 
Sag of line wire, 391. 
Saturation point of magnetisation, 

116. 
Schaffhausen, power of falls at, 

12, 14. 
Schmidmer's joint for line wires, 

397. 
Secohm-meter, 240. 

, unit of self-induction, 220. 

Secondary cells, use of, 3. 
Self-induction, 76, 163, 218-220, 

243, 248, 256, 349, 356, 364. 
experiments with Gris- 

com motors, 77. 
Self-regulating dynamo, 161. 
motor, 173, 178, 180, 

182. 



Self -regulation of shunt- wound 
motor, range of, 158. 

— of two series machines, 

199. 

Self -starting of rotary field motors, 
313. 

Series system of distribution, 169. 

Series-wound machines, self -regu- 
lation of two, 199. 

motor, 75. 

regulation of speed 

of, 150. 

Shell, equivalent magnetic, 40. 

Shunt-wound motor, 75. 

not self -starting, 160. 

with over-compounded 

generator, 161. 

range of self-regulation, 



158. 

speed of, for maximum 

commercial efficiency, 157. 

Shuttle-wound or Siemens' arma- 
ture, 73. 

Siemens' dynamo, 406. 

Hopkinson's charac- 
teristics, 142, 144. 

field magnet, Fig. 29. 

shuttle- wound armature, 73. 



Silicon-bronze wire, 390. 

Sine curve of E.M.F. best form, 

384. 
of a revolving field, 

301. 
Single-phase motors, 355, 384. 

Arno's tests of Brown's, 



366. 



tion, 364. 



Necessity of self-induc- 



Starting devices for, 
367. 
" Slip," efficiency and, 330. 

magnetic, of armature, 302, 

305, 322, 353. 

Soft iron, 30. 

Solder for Weiller's joint, 397. 
Sparking, prevention of, 160. 
Spasmodic governors, 171. 
Speed characteristic, 145. 

constant, under varying 

load, 160. 

independent of current, 103, 



180. 



444 



INDEX. 



Speed, regulation of, in revolving 
field, 303. 

torque as a function of, 345. 

of motors, determination 

of efficiency by, inaccuracy of, 
56. 

determining conditions 



for, 53. 



age, 188. 



having regard to leak- 



regulation of, 150, 156. 

Speed and torque of rotary field 
motors, relation of, 314. 

Squirrel-cage winding, 304, 321. 

"Star-coupling," 342, 416, 418. 

Starting device for motor, 205. 

devices for single-phase mo- 
tors, 367. 

power of a motor, 53. 



Static characteristic, 136, 
Steam-power of United States, 

15. 

of world, 13. 

Steel, cast, conductivity and 

strength of, 391. 
Steinmetz' formula for capacity of 

overhead lines, 281. 
Strength of conductors, 391. 
Stress, mechanical, on alternating 

motor, 266. 

in line wire, 391. 

Sturgeon and Barlow's wheel, 

61. 
Sugar-refinery, motors for, 430. 
Sumpner and Ayrton's test for 

power of alternators, 225. 
Switzerland, utilization of water- 
power in, 13. 
Systems of transmission of energy, 

167. 

Tables, experiments on self-in- 
duction, 79-81. 

Temperature co- efficient of cop- 
per, 392. 

Tesla's system of power trans- 
mission, 291. 

Test for Lag, Blakesley's, 238. 

for power of alternators, 

methods of, 225, 229. 

for power by Wattmeter, 



233, 236. 



Thompson's (Prof. S.) horse-power 

curves, 143. 
graphic comparison of work 

and efficiency, 152. 
Thomson's (Elihu) lightning 

guard, 400. 
Three ampere - meter test for 

power, 229. 
Three-phase generator, Oerlikon, 

424. 

motors, 293, 301, 339, 351, 



389. 



advantage of, 341. 



Three voltmeter test for power of 

alternators, 225. 
Thury dynamo, 419. 
Torque, 53, 100, 174, 314, 362. 

M. Deprez on, 101. 

Diagram of single - phase 

motor, 362. 

and efficiency, relation of, 



322, 334. 

— independent of speed, 103. 

— and induction, 317. 
and speed, relation of, in 



rotary field motors, 314, 

345. 
Tramways, electric, 19. 
Transformers, 210, 419. 

cooling of, 427. 

Oerlikon, 425. 

Transmission of energy, cost of 

line for, 370. 

general principles, 1. 

importance of alter- 
nating currents for, 208, 255. 

margin of power for 



alternators, 263. 

maximum efficiency of 

alternators, 261. 

systems of, 167. 

, , cost of line for 



various, 389. 

Tesla's system, 291. 



"Trolley" system, 20. 

Trotter, Goolden and, field mag- 
net, Fig. 35. 

Two -phase motors compared with 
continuous current, 384, 389. 

three-phase, 



301, 339. 



invention of, 289, 



INDEX. 



445 



Underground lines essential in 

populous districts, 389. 
Uni-polar dynamo, 65. 
Unit, current, 40, 41, 60. 

electro -motive force, 43, 60. 

line of force, 31, 34. 

Unit magnetic field, 33, 34. 
pole, definition of, 33, 

37. 

of capacity— -farad, micro- 
farad, 60. 

- of current — ampere, 60. 
of electromotive force — volt, 



60. 

of energy — erg, 34. 

of force — dyne, 34. 

of power — watt, 60. 

of quantity — coulomb, 60. 

of resistance — ohm, 60. 

of self-induction, 220. 

United States, water and steam- 
power of, 15. 

Varying load, constant speed 

with, 160, 202. 
investigation of effect 

of, on alternating motor, 268. 
Virtual pressure, 215. 
Volt — unit of electromotive force, 

60. 
Volts, conversion from absolute 

system, 105. 
Voltage, constant, investigation 

of "perfect motor," 328. 

of practical motor, 



331, 



from multipolar machines, 
132. 
Voltmeter, three, test for power 
of alternators, 225. 

Water-power, resources from, 
12. 



Water-power of United States, 

15. 
Watt, conversion from absolute 

system, 105. 

unit of power, 60. 

Wattmeter, 231, 233. 

correction for tests by, 239. 

Weber on theory of magnetisa- 
tion, 28. 

Weight of line conductor for eco- 
nomical transmission, 380. 

of self-regulating motor, 

comparative, 178. 

Weiller's joint coupling, 396. 

Wenstrom's dynamo, 417. 

Westinghouse lightning guard, 
400. 

Weston field magnet, 113, Fig. 
41. 

Weston machines, 108. 

Whirl, magnetic, 37. 

Wiedemann on theory of magne- 
tisation, 28. 

Windage, 107. 

Winding of armatures, insulation 
of wires for, 191. 

of gramme armature, 89. 

of armatures, " squirrel - 

cage," 304, 321. 

Wires, line, binding-in, 394. 

joints for, 395. 

materials for, 390. 

Wirt lightning guard, 398. 
Wolverhampton dynamo, 406. 
Work, dissipation of, 214. 

heavy, need of weak field 

magnets for motor, 176. 

maximum, and maximum 



efficiency, 148. 

from motor, 51, 153. 



Workshops, method of applying 

electric power in, 18. 
World, steam-power of, 13. 



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